A communication unit for soft-decision demodulation and method therefor

ABSTRACT

A communication unit for performing soft-decision demodulation comprises a receiver that receives a transmitted signal having a first set of bits comprising k bits, selected from a set of 2k possible signals according to values of the k bits, and a second set of bits comprising Qm bits based on a phase rotation of the transmitted signal selected from a set of 2Qm possible rotations. The receiver comprises: a demodulator comprising a bank of 2k correlators and is configured to: detect a transmission of each possible transmitted signal, and output 2k phases of the correlator outputs as a third set of inputs. A de-mapper circuit receives the third set of inputs: determines statistics derived from a number of aggregated correlator output phase distributions of the third set of inputs; and calculates and outputs a second set of aposteriori soft bits comprising Qm soft bits.

FIELD OF THE INVENTION

The field of the invention relates to a communication unit forsoft-decision demodulation and decoding of communication packets in areceiver chain. The field of the invention is applicable to, but notlimited to, demodulation for current and future generations ofcommunication standards.

BACKGROUND OF THE INVENTION

Orthogonal Signalling (OS) is a known communications technique. In atransmitter of a communication unit that employs OS, a sequence of kbits (each of the k bits having a value ‘0’ or ‘1’) is converted into aninteger in a range ‘0’ to ‘2^(k)−1’ using binary to decimal conversion.This integer is then used as an index to select a particular one of2^(k) communication sequences to transmit. In OS, the set of 2^(k)communication sequences are designed to be orthogonal to each other,such that they can be readily distinguished from each other. Theselected one of the 2^(k) communication sequences is transmitted over acommunication channel, which may impose distortion upon it owing to theeffects of noise, interference, dispersion, fading, Doppler, etc. As aresult, the received sequence will typically differ from the transmittedsequence to some degree and the orthogonality of the sequences may notbe preserved.

In the corresponding OS receiver, a bank of 2^(k) correlators is used.Each correlator compares the received signal with a corresponding one ofthe 2^(k) orthogonal communication sequences, which are known to thereceiver. Each of the 2^(k) correlators produces a correlation metric,which will adopt a magnitude that quantifies the strength of thecorrelation between the received signal and the corresponding one of the2^(k) orthogonal communication sequences. More specifically, a highmagnitude indicates a high correlation and, hence, a high confidencethat the corresponding one of the 2^(k) orthogonal communicationsequences was the one that was transmitted. By contrast, a low magnitudeindicates a low correlation and, hence, a low confidence that thecorresponding one of the 2^(k) orthogonal communication sequences wasthe one that was transmitted. The receiver compares the 2^(k) magnitudesoutput by the bank of 2^(k) correlators to identify the one having thehighest magnitude. The index of the correlator producing the highestmagnitude is identified in the range 0 to 2^(k)−1. Finally, a harddecision on the values of the bits in the sequence of k bits is obtainedby performing decimal to binary conversion on the index of thecorrelator producing the highest magnitude.

In a conventional OS communications scheme when the channel conditionsare favourable, it may be expected that the received sequence will besimilar to the one of the 2^(k) orthogonal communication sequences thatwas selected to be transmitted. In this case, it may be expected thatonly the correct one of the correlators in the receiver's bank of 2^(k)correlators will produce an output having a high magnitude and that thedecimal to binary conversion will identify the correct bit sequence,without errors.

However, when the channel conditions are unfavourable, it may be thatthe received sequences will not be very similar to any of the 2^(k)orthogonal communication sequences, but that it may be somewhat similarto two or more of them, which may or may not include the one of the2^(k) orthogonal communication sequences that was selected to betransmitted. In this case, two or more of the correlators in thereceiver's bank of 2^(k) correlators will produce an output having arelatively high magnitude and the correct one may not have the highestmagnitude, particularly in the case where the channel does not preservethe orthogonality of the communication sequences. In this case, thedecimal to binary conversion will identify an incorrect bit sequence,containing some bit errors. This may be mitigated by applying a channelencoder in the transmitter, to encode the bit sequence, before mappingit onto an OS sequence. In the receiver, the recovered bit sequence maythen be passed through a corresponding channel decoder, in order tomitigate the bit errors that result from unfavourable channelconditions.

However, it is well understood that a channel decoder's ability tocorrect bit errors is limited, when operating on the basis of harddecisions. Suppose that in an OS scheme, the received sequence wassimilar to two of the 2^(k) orthogonal communication sequences, namelyslightly less similar to the correct one of the 2^(k) orthogonalcommunication sequences and slightly more similar to an incorrect one ofthe 2^(k) orthogonal communication sequences. In this case, themagnitudes output by the two corresponding correlators will be similar,but the incorrect one will be slightly higher. During the generation ofthe hard decisions through decimal to binary conversion, the onlyknowledge preserved is that a particular one of the correlators had thehighest magnitude. The knowledge that two of the correlators had similarmagnitudes will be lost, and the channel decoder will be deniedknowledge that there was another (slightly less likely) sequence of kbits that was also a candidate.

In order to resolve this, it is known that a soft-decision channeldecoder provides a stronger error correction capability, provided thatthe receiver can provide soft-decisions. These soft decisions expressnot only what the most likely value of each bit is (like a hard-decisionreceiver), but also how likely that value is (unlike a hard-decisionreceiver). More specifically, the magnitudes output by the bank of 2^(k)correlators can be used to determine the likelihood of each of thecorresponding 2^(k) orthogonal communication sequences being correct andthen these likelihoods can be converted into likelihoods of each of thek bits having a value of 0 or 1.

However, the inventors of the present invention have identified that theliterature lacks a mathematically rigorous and robust method forconverting the magnitudes output by the bank of 2^(k) correlators intothe likelihood of each of the corresponding 2^(k) orthogonalcommunication sequences and then converting these into the likelihoodsof each of the k bits having a value of 0 or 1.

SUMMARY OF THE INVENTION

In some implementations, the present invention provides soft-decisiondemodulators and methods for soft-decision demodulation using aggregatedcorrelator output distributions, for example with improved quality ofsoft-decisions.

In particular, examples of the present invention describe estimations ofthe aggregated correlator output distributions and their use forsoft-decision demodulation. These and other aspects of the inventionwill be apparent from, and elucidated with reference to, the exampleembodiments described hereinafter.

In a first aspect of the invention, a communication unit for performingsoft-decision demodulation comprising a receiver is described. Thereceiver is arranged to receive a transmitted signal having a first setof bits comprising k bits that has been selected from a set of 2^(k)possible signals according to values of the k bits, and includes asecond set of bits comprising Q_(m) bits based on a phase rotation ofthe transmitted signal selected from a set of 2^(Qm) possible rotations.The receiver comprises: a demodulator comprising a bank of 2^(k)correlators and configured to: detect a transmission of each possibletransmitted signal, and output 2^(k) phases of the correlator outputs asa third set of inputs. The receiver also comprises a de-mapper circuitcoupled to the demodulator and configured to receive the third set ofinputs; determine statistics derived from a number of aggregatedcorrelator output phase distributions of the third set of inputs, andcalculate therefrom and output a second set of aposteriori soft bitscomprising Q_(m) soft bits. In this manner, high quality soft-decisionscan be obtained in a robust and practical manner, which is not dependenton and sensitive to an excessive number of correlator output phasedistributions.

In an optional example, the number of aggregated correlator output phasedistributions is one, and the aggregated correlator output phasedistribution approximates the aggregation of the 2^(k) distributions ofthe output phases of the 2^(k) correlators when the corresponding one ofthe 2^(k) possible signals was selected as the transmission signal. Inthis manner, the number of correlator output magnitude distributionsbecomes small, leading to a high degree of practicality and robustness.wherein the aggregated correlator output phase distribution isrepresented by a second set of distribution parameters.

In an optional example of the communication unit, the aggregatedcorrelator output phase distribution may be represented by a second setof distribution parameters. In this manner, rather than using ahistogram to represent each correlator output phase distribution, theamount of information required to represent each correlator output phasedistribution becomes small, leading to a high degree of practicality androbustness. Furthermore, the fitting function used to generate theparameters may be able to fill in the gaps between samples, leading toincreased robustness.

In an optional example of the communication unit, the second set ofdistribution parameters may comprise a spreading parametersigma_(phase). In this manner, the amount of information required torepresent each correlator output phase distribution becomes small atjust one parameter, leading to a high degree of practicality androbustness.

In an optional example of the communication unit, the demodulator isfurther configured to output 2^(k) magnitudes of correlator outputs,based on the detected possible transmitted signals, by the bank of 2^(k)correlators as a first set of inputs. In this manner, the magnitudes ofthe correlator outputs become available for classifying the correlatoroutputs, in order to aid the estimation of their aggregateddistributions.

In an optional example, the de-mapper circuit may be configured toperform at least one of the following: estimate the second set ofdistribution parameters of the aggregated correlator output phasedistribution by fitting a fifth probability distribution to phase errorsof correlator outputs obtained by correlating received synchronisationsignals with known synchronisation signals; estimate the second set ofdistribution parameters of the aggregated correlator output phasedistribution by fitting a sixth probability distribution to phase errorsof correlator outputs having the greatest magnitude among sets of 2^(k)correlator outputs obtained by the bank of 2^(k) correlators; select thesecond set of distribution parameters of the aggregated correlatoroutput phase distribution from a look-up-table coupled to the de-mappercircuit. In this manner, the receiver does not need to have priorknowledge of the distribution parameters and can instead estimate thembased on the received signal, leading to a high degree of practicality.

In an optional example of the communication unit, at least one of thefifth or sixth probability distributions may be the Gaussiandistribution. In this manner, a strong resemblance to the distributionof real signals may be expected, leading to high quality soft-decisionsand increased robustness.

In an optional example, the output phases of the 2^(k) correlators maybe combined with the second set of distribution parameters of theaggregated correlator output phase distribution in order to obtain athird set of apriori soft signals comprising 2^(k+Qm) soft phases. Inthis manner, the contribution of each correlator output to thesoft-decision demodulation can be expected to be commensurate to theappropriate level of confidence that they provide, leading to highquality soft decisions.

In an optional example, the de-mapper circuit may be configured toaccept a fourth set of apriori soft signals comprising Q_(m) soft bitsas a fourth set of inputs. In this manner, feedback information providedby a channel decoder can enhance the soft-decision demodulation in aniterative manner, leading to high quality soft decisions.

In an optional example, the second set of aposteriori soft bits may becombined with the soft bits of the fourth set of apriori soft signals,in order to obtain a second set of extrinsic soft bits comprising Q_(m)soft bits. In this manner, a positive feedback loop between the channeldecoder and the soft-decision demodulator is avoided, leading to highquality soft decisions.

In an optional example, the communication unit may combine all apriorisoft signals to generate a set of 2^(k+Qm) aposteriori soft signals andwherein the set of 2^(k+Qm) aposteriori soft signals may be combined toobtain the first set of aposteriori soft bits and the second set ofaposteriori soft bits. In this manner, all available information makesan appropriate contribution to the soft decisions, leading to highquality soft decisions.

In a second aspect of the invention, a method for performingsoft-decision demodulation comprising a communication unit having areceiver, the receiver having a de-mapper circuit coupled to ademodulator that comprises a bank of 2^(k) correlators, is described.The method at the receiver comprises: receiving a transmitted signalthat conveys a first set of bits comprising k bits that has beenselected from a set of 2^(k) possible signals and a second set of bitscomprising Q_(m) bits based on a phase rotation of the transmittedsignal selected from a set of 2^(Qm) possible rotations: detecting atransmission of each possible transmitted signal; outputting 2^(k)phases of correlator outputs, based on the detected possible transmittedsignals, by the bank of 2^(k) correlators as a third set of inputs;receiving the third set of inputs, determining statistics derived fromone aggregated correlator output phase distribution of the third set ofinputs that approximates an aggregation of a 2^(k) distributions of theoutput phases of the bank of 2^(k) correlators when the correspondingone of the set of 2^(k) possible signals was selected as thetransmission signal; and calculating therefrom and output a second setof aposteriori soft bits comprising Q_(m) soft bits.

BRIEF DESCRIPTION OF THE DRAWINGS

Further details, aspects and embodiments of the invention will bedescribed, by way of example only, with reference to the drawings. Inthe drawings, like reference numbers are used to identify like orfunctionally similar elements. Elements in the FIG's are illustrated forsimplicity and clarity and have not necessarily been drawn to scale.

FIG. 1 illustrates a top-level block diagram of an OS-schemetransmission system adapted according to example embodiments of thepresent invention.

FIG. 2 illustrates examples of: a) maximum, and b) two aggregated,approaches in obtaining distributions of the correlator outputs of theOS-scheme transmission system of FIG. 1 .

FIG. 3 illustrates a multipath (MP) channel dataset of MP −7.5 dB withcorrect correlated data for the OS scheme of FIG. 1 , using a histogram& Rician distribution fit.

FIG. 4 illustrates an MP −7.5 dB dataset incorrect correlated data forthe OS scheme of FIG. 1 , using a histogram & Rician distribution fit.

FIG. 5 illustrates the distributions of OS-scheme of FIG. 1 correlatoroutputs for an additive white gaussian noise (AWGN) channel of thedatasets of FIG. 3 and FIG. 4 .

FIG. 6 illustrates the distributions of OS-scheme of FIG. 1 correlatoroutputs for a Multipath communications channel for the datasets of FIG.3 and FIG. 4 .

FIG. 7 illustrates a conversion to OS symbol LLRs for the AWGN channelfor the OS-scheme datasets of FIG. 5 .

FIG. 8 illustrates a conversion to OS symbol LLRs for a Multipathcommunications channel for the OS-scheme datasets of FIG. 6 .

FIG. 9 illustrates a top-level block diagram of an alternative OS-schemetransmission system adapted according to example embodiments of thepresent invention.

FIG. 10 illustrates a testbench block diagram for an example 16OS scheme(orthogonal signalling with M=16).

FIG. 11 illustrates a sample extrinsic information transfer (EXIT)chart, for an example 16OS-scheme dataset with true and estimatedchannels, both as AWGN_-7.5 dB.

FIG. 12 illustrates EXIT charts for the 16OS-scheme dataset [5] withdifferent estimated and true signal-to-noise ratio (SNR) values on anAWGN channel.

FIG. 13 illustrates EXIT charts for the 16OS-scheme dataset [5] with thesame estimated and true SNR values on the AWGN channel.

FIG. 14 illustrates EXIT charts using the 16OS-scheme dataset [5] withthe same estimated and true SNR values on the Multipath channel.

FIG. 15 illustrates a top-level block diagram of an OS-PSK transmissionsystem according to another example embodiment of the present invention.

FIG. 16 illustrates distributions of correct and incorrect 16OS-QPSKcorrelator magnitudes for the MP_-7.5 dB dataset.

FIG. 17 illustrates distributions of correct and incorrect 16OS-QPSKcorrelator phase errors for the MP_-7.5 dB dataset.

FIG. 18 illustrates an example 16OS-PSK testbench.

FIG. 19 illustrates an example 16OS-nPSK channel simulation.

FIG. 20 illustrates per-scheme EXIT charts for the 16OS-QPSK scheme.

FIG. 21 illustrates the magnitude distributions of the 16OS-PSK-schemecorrelator outputs for the AWGN channel.

FIG. 22 illustrates the phase error distributions of the 16OS-PSK-schemecorrelator outputs for the AWGN channel.

FIG. 23 illustrates the magnitude distributions of the 16OS-PSK-schemecorrelator outputs for the Multipath channel.

FIG. 24 illustrates the phase error distributions of the 16OS-PSK-schemecorrelator outputs for the Multipath channel.

FIG. 25 illustrates the EXIT charts of the OS-PSK scheme for theMultipath channel.

FIG. 26 illustrates an AWGN_0 db dataset for an example OS scheme,illustrating a first 20 rows out of 8100, according to some exampleembodiments of the invention.

FIG. 27 illustrates a correlator output distribution of alargest-magnitude method, according to some example embodiments of theinvention.

FIG. 28 illustrates 4-bit message combinations and corresponding symbolLLR parameters, according to some example embodiments of the invention.

FIG. 29 illustrates terms in a bit LLR calculation, when there is nofeedback from a decoder, according to some example embodiments of theinvention.

FIG. 30 illustrates 4-bit message combinations, with correspondingsymbol LLR parameters and apriori bit LLR combinations, according tosome example embodiments of the invention.

FIG. 31 illustrates a AWGN_0 db dataset of a 16OS-QPSK schemeillustrating a first rows out of 8100, according to some exampleembodiments of the invention.

FIG. 32 illustrates terms in a symbol-bit LLR conversion for 6-bitmessages of FIG. 31 , according to some example embodiments of theinvention.

FIG. 33 illustrates the 6-bit message combinations and corresponding LLRparameters, according to some example embodiments of the invention.

FIG. 34 illustrates a conversion of apriori bit LLRs into a symbol LLRdomain, according to some example embodiments of the invention.

FIG. 35 illustrates a flowchart of a soft demapping approach for an OSscheme, according to some example embodiments of the invention.

FIG. 36 illustrates a flowchart of a soft demapping algorithm for anOS-PSK scheme, according to some example embodiments of the invention.

FIG. 37 illustrates a typical computing system that may be employed inan electronic device or a wireless communication unit to perform softdemapping and channel decoding in accordance with some exampleembodiments of the invention.

DETAILED DESCRIPTION

In order to mitigate the problem that the literature lacks amathematically rigorous and robust method for converting the magnitudesoutput by a bank of 2^(k) correlators into a likelihood of each of thecorresponding 2^(k) orthogonal communication sequences, and thenconverting these into the likelihoods of each of the k bits having avalue of 0 or 1, the inventors of the present invention have describedthe following in a first section of the description. A communicationunit and method for performing soft-decision demodulation, comprising areceiver for communicating on a communication channel with anothercommunication unit, is described. The receiver is arranged to receive atransmitted signal conveying a first set of bits comprising k bits thathas been selected from a set of 2^(k) possible signals. The receiverincludes a demodulator comprising a bank of 2^(k) correlators andconfigured to: detect a transmission of each possible transmittedsignal, and output 2^(k) magnitudes of correlator outputs, based on thedetected possible transmitted signals, by the bank of 2^(k) correlatorsas a first set of inputs. The receiver also includes a de-mapper circuitcoupled to the demodulator and configured to receive the first set ofinputs; determine statistics derived from a plurality of aggregatedcorrelator output magnitude distributions of the first set of inputs,wherein the plurality of aggregated correlator output magnitudedistributions is fewer than 2^(2k); and calculate therefrom and output afirst set of aposteriori soft bits comprising k soft bits. In thismanner, a first solution provides a soft demapping approach for OS-onlycorrelator outputs that enables high quality soft-decisions to beobtained in a robust and practical manner, which is not dependent on andsensitive to an excessive number of correlator output magnitudedistributions.

In addition, in a second section of the description, a soft-decisionapproach in demapping of a demodulator's correlator outputs from anorthogonal signalling-phase-shift keying (OS-PSK) modulation scheme intoextrinsic soft bits in the form of logarithmic likelihood ratios(LLRs)—also known as bit LLRs or soft bits is described, according tosome examples of the invention. Here, a Convert to PSK symbol LLRscircuit and a Symbol-to-symbol LLR circuit may additionally be used,whereby a transmitter chain applies a direct-sequence spread spectrum(DSSS) technique and a modulator circuit converts information bits intoOS-PSK modulated data. In this manner, the extrinsic soft bits producedfor the PSK-modulated bits are consistent with those produced for theOS-modulated bits, expressing a relatively appropriate level ofconfidence in the bit values.

Correlator Distribution Investigation and Conversion to Symbol LLRs: OSScheme

Referring now to FIG. 26 , a top-level block diagram of an OS-schemetransmission system that has been adapted according to exampleembodiments of the present invention is illustrated. Example embodimentsof the present invention provide a receiver circuit in a receiver 102 ofan Orthogonal Signalling (OS) transmission system 100 that detects eachreceived OS signal using a bank of correlators and demaps the correlatoroutput values into a set of soft bits 103, where the soft bits 103 arefed into a soft-decision channel decoder 104. In some examples, thisdemapper operates in a receiver circuit for performing soft-decisiondemodulation in a transmission system 100 comprising a transmitter 105,a channel 106 and a receiver 102, wherein the transmitter signals a setof bits 107 comprising k bits by transmitting an OS transmission signal108 that is selected from a set of 2^(k) possible signals according tothe values of the k bits. The receiver 102 uses a bank of 2^(k)correlators to detect the transmission of each possible signal, andwherein the 2^(k) magnitudes of the correlator outputs 109 are providedas a set of inputs to the demapper circuit 113 The demapper circuit 113calculates a set of aposteriori soft signals 110 based on statistics andparameters 111 derived from a plurality of aggregated correlator outputmagnitude distributions.

In some examples, the aggregation operation is not directly in the flowfrom received correlator outputs to soft-demodulated LLRs. Instead, insome examples including the illustrated example, the aggregation may beperformed upon the statistics of the channel, for example in advanceduring an offline look up table process, or for example in advance usingan online channel estimation process. For completeness it is confirmedthat only the distribution parameters (e.g., s and sigma) extracted fromthe aggregation that are used in the direct flow from input to output.In some examples, the demapper circuit 113 is referred to as a softdemapper, since it generates soft signals. These soft signals may thenbe converted into soft bits 103, according to an example process that isdemonstrated in the flowchart of FIG. 35 and is described later.

In this way, examples of the present invention provide a mathematicallyrigorous and robust circuit architecture and method of converting themagnitudes output by a bank of 2^(k) correlators into a likelihood ofeach of the corresponding 2^(k) orthogonal communication sequences andthen converting these into the likelihoods of each of the k bits havinga value of ‘0’ or ‘1’, thereby addressing the problem described in thebackground section.

In examples of the invention, investigations were carried out on thedistributions of a demodulator's correlator outputs (also referred to as‘cross-correlation values’) in order to identify the possibilities ofusing the distribution characteristics for the soft demapping ofcorrelator outputs into soft signals that may be used to generate softbits. Also, as part of soft demapping, a circuit was developed (inMatlab) that converts the magnitudes of the correlator outputs into aset of soft magnitudes in a form of logarithmic-likelihood ratios(LLRs), in one example embodiment, by using a plurality of aggregatedcorrelator output magnitude distributions.

Examples of the invention focus on two parts of FIG. 1 , namely:characterising the ‘Modulation-channel-specific library of correlatordistributions’ look up table 112 (also identified in step 4406 in FIG.35 ), and development of the demapper circuit 113 arranged to convertthe correlator outputs to OS symbol LLRs (also identified in step 4411).

A skilled artisan in this field may implement some of the hereafterdescribed circuits in hardware, firmware or software, such as CRC,encoder, bits-to-symbols circuit, modulator, demodulator, correlator anddecoder. Hence, the various ways that these circuits can be implementedwill not be described in any more detail than is necessary for a skilledperson to replicate the concepts described herein.

Data

In order to model the transmitter and the channel, six datasets ofcorrelator output values of a demodulator were used, obtained withdifferent channel conditions, where the datasets were provided by [5].These datasets are based on three signal-to-noise ratio (SNR) values of0 dB, −3 dB and −7.5 dB, and based on two channel models: the additivewhite Gaussian noise (AWGN) channel and the multipath (MP) channel. Thedata is generated based on an M-ary orthogonal signalling (OS)transmission scheme for M=16 (as shown in FIG. 1 ), where M is a powerof 2. This means that every k=log₂(M)=4 bits is converted in bits tosymbol circuit 114 into an OS symbol in the transmitter 105. Thedatasets are represented in this document using the following notations:AWGN_0 dB, AWGN_−3 dB, AWGN_−7.5 dB, MP_0 dB, MP_−3 dB, MP_−7.5 dB.

Referring for example to FIG. 26 , an AWGN_0 db dataset for an exampleOS scheme illustrates a first 20 rows out of 8100, according to someexample embodiments of the invention. For example, FIG. 26 shows thefirst twenty rows 3501 of the dataset AWGN_0 db, where each dataset has8100 rows of data. Each row in a dataset has one symbol (with a value3502 in a range [0,M−1] or [0,15]) and corresponding one of M=16transmitted codes (with indices in a range [0,M−1] or [0,15]) wherethere is a cross-correlation magnitude 3503 for each of the 16 codes.Although this example embodiment uses M=16, it is envisaged that theconcepts and definitions described herein can be applied to any value ofM=2^(k).

Amongst the M=16 correlator outputs per symbol, the correlator outputwith the transmitted code index is assumed to be equal to the symbolvalue as the “correct” correlator output, as shown by the bold numbersin FIG. 26 . The remaining M−1=15 correlator outputs in the row for thatsymbol are assumed to be the “incorrect” correlator outputs, asdemonstrated by the non-bold correlator values in FIG. 26 . For example,the 16^(th) row 3504 in FIG. 26 has a symbol value ‘5’ (perhaps for a4-bit message “0101”), for which the transmitted code with the index 5is the correct correlator, with a magnitude of 49.9. For the samesymbol, codes of indices in the range [0, 4] V [6, 15] are the incorrectcorrelator outputs, with magnitudes in the range [6.0, 13.2]. Theanalogy of correct and incorrect can be understood in this high-SNRexample, where the code with the highest cross-correlation magnitudenearly always has the ‘correct’ index.

As shown in FIG. 1 , the demapper circuit 113 is arranged to receivesthe magnitudes of the correlator outputs 109 as an input, and hasknowledge of the parameters 111 of the aggregated correlator outputmagnitude distributions (which are shown as an additional input in FIG.1 ) and converts the correlator outputs to OS symbol LLRs. Hereafter,the term ‘circuit’ is intended to encompass any electronic circuit orcomponent or arrangement of logic gates, modules, function in hardwareor firmware, as well as any function implemented as a softwareoperation, noting that various implementations of the concepts describedherein may be implemented using either hardware, firmware, software orany combination thereof, for example depending upon the prevailingapplication, use, etc., as would be understood to those skilled in theart. In order to support the later discussion of the “Convert to OSLLRs” circuit, this section details the correlator output distributions.More specifically, a later section details an aggregation of thecorrelator output distributions, according to some example embodimentsof the present invention. Following this, a later section details theparameterisation of the aggregated correlator output distributions,allowing the aggregated distributions to be described using a smallnumber of parameter values, according to some example embodiments of thepresent invention. Finally, a later section discusses how the parametervalues may be estimated in practical applications, according to someexample embodiments of the present invention.

Number of Distributions

The maximum number of distributions that can be used to calculate OSLLRs for k-bit transmissions is 2^(2k), as explained in the following.Given the relatively large number of symbols (resembling transmissions)in each of the six datasets (with 8100 rows), there are several rows foreach symbol value, and hence there exists several sets of M=16correlator outputs per symbol value. For example, there are four rows3505 in FIG. 26 with a symbol value of ‘7’. The way to obtain themaximum number of distributions is to, for every symbol value and fromall dataset rows with this symbol value, obtain the distribution of allcorrelator values with code index ‘0’, obtain the distribution of allcorrelator values with code index ‘1’, and so on to code index M−1=15.This way, every symbol value, will have M=16 distributions of correlatoroutputs, where one corresponds to the correct correlator outputs and theother M−1 (or fifteen) correspond to the incorrect correlator outputs.This is shown in FIG. 2 at (maximum distributions approach) 201, whereFIG. 2 illustrates a) maximum distribution 201, and b) two aggregateddistribution 202, approaches in obtaining distributions of thecorrelator outputs. As there are M=16 symbol values, there will be anoverall of M*M or 2^(2k)=256 distributions for one dataset using thisapproach, as shown in FIG. 2 . In this figure, the rows in the top(maximum distribution) approach 201 correspond to different symbolvalues, and columns show different code indices. Notably, thedistributions on the diagonal line 203 belong to the correct correlatoroutputs, and the incorrect correlator outputs are characterised by theremaining 2^(2k)−2^(k) distributions 204 in FIG. 2 .

It is also possible to aggregate the 2^(2k) distribution into just twodistributions for calculating symbol LLRs: (i) the aggregation of thedistributions of all the correct correlator output values 205, and (ii)the aggregation of the distributions of all the incorrect correlatoroutput values 206, as illustrated and referred to as a two aggregateddistributions approach 202. Here, in this two aggregated distributionsapproach 202, the distributions will not be specific to a single symboland instead show the characteristics of data corresponding to allsymbols. Also, the incorrect distribution will not be specific to asingle code index and represents incorrect correlator outputs for allcode indices. This contrasts with the maximum distributions approach201, which had a separate distribution for each pair of ‘sentsymbol-correlator index’. In the two aggregated distributions approach202, the incorrect 206 and correct 205 distributions provide collectiverepresentations of their corresponding distributions in the maximumdistributions approach 201, as shown in FIG. 2 . The maximumdistributions approach 201, compared to the two aggregated distributionsapproach 202, therefore provides a more specific representation of thecorrelator output values. However, the maximum distributions approach201 comprises M²=256 distributions, each of which is parameterised by afew parameters, which in some examples of the invention may beconsidered to introduce excessive complexity. A further concern in someexamples may be that the maximum distributions approach may be overtuned and may not be robust to varying channel conditions. Note that anassumption of the two aggregated distributions approach 202 is that thecorrect distributions of the M=16 symbols are all similar to each otherand that the remaining incorrect distributions are all similar to eachother. In experiments the inventors of the present invention found thatthis assumption is sufficiently valid to enable good operation.

In summary, in some examples, a two aggregated distributions approach202 is proposed, wherein the plurality of aggregated correlator outputmagnitude distributions is two, and wherein the first aggregatedcorrelator output magnitude distribution approximates the aggregation205 of the 2^(k) distributions on the diagonal line 203 of the outputmagnitudes of the 2^(k) correlators when the corresponding one of the2^(k) possible signals was selected as the transmission signal, andwherein the second aggregated correlator output magnitude distributionapproximates the aggregation 206 of the 2^(2k)−2^(k) distributions 204of the output magnitudes of the 2^(k) correlators when the correspondingone of the 2^(k) possible signals was not selected as the transmissionsignal.

Fitting Distributions to Data

In some examples of the invention, in order to fit distributions to thecorrelator outputs from the six datasets of correlator output values ofa demodulator used to model the transmitter and the channel, eachdataset is divided into two sets of values: the set of all correctcorrelator outputs and the set of all incorrect correlator outputs,according to the two aggregated distributions approach described above.Through investigations, to each of the two correlator sets of data, andfor all datasets, several distributions (such as normal, Rayleigh,Rician, etc) have been fit using Matlab's fitdist command. The completelist of distributions considered can be found at:https://www.mathworks.com/help/stats/fitdist.html#btu538h-distname.Based on visual observation it was concluded that normal and Rayleighdistributions are good fits for the correct and incorrect sets ofcorrelator data, respectively. In the example investigations, since thenormal and the Rayleigh distributions are both special cases of theRician distribution, it was also concluded that the Rician distributionfits both correct and incorrect data. All the other distributionsaccepted by the fitdist command (a total of 24 accepted distributions)did not fit well to the data, unless they were also generalisations ofthe Rician distribution. More specifically, it was found that theNakagami and Weibull distributions were also good fits for the incorrectdata, but they do not also generalise the normal distribution and sothey do not offer good fits for the correct data.

Given that the Rician distribution is a generic case of both normal andRayleigh distributions, the Rician distribution was chosen in someexamples of the invention so that comparisons can be made betweencorrect and incorrect sets of correlator outputs. The Riciandistribution has two parameters, the non-centrality parameter(s) and thescale parameter (σ), with similar analogies to the mean and varianceparameters of normal distributions. Therefore, for each dataset therewill be four distribution parameters of the correlator outputs; s_(corr)and σ_(corr) of the correct correlator outputs distribution, ands_(incorr) and σ_(incorr) of the incorrect correlator outputsdistribution. Note that Rician distributions with certain conditions arespecial cases of some distributions in the chi family of distributions.For example, assuming a random variable R is Rician distributed with anon-centrality parameters and a scale parameter σ=1, R also follows anoncentral chi distribution with two degrees of freedom, and R² willhave a non-central chi-squared distribution with two degrees of freedomand a non-centrality parameter s². Therefore, a set of correlator outputvalues with a Rician distribution of σ=1 can be modelled using thementioned chi and chi-squared distributions.

Referring now to FIG. 3 and FIG. 4 , FIG. 27 illustrates a multipath(MP) channel dataset of MP −7.5 dB with correct correlated data for theOS scheme of FIG. 1 , using a histogram & Rician distribution fit andFIG. 28 illustrates an MP −7.5 dB dataset incorrect correlated data forthe OS scheme of FIG. 1 , using a histogram & Rician distribution fit.In order to demonstrate the distribution of correlator output datagraphically, two graphs are plotted for each dataset, correct data 300is illustrated in FIG. 3 and incorrect data 400 is illustrated in FIG. 4for the MP_-7.5 dB dataset of the OS-scheme transmission system of FIG.1 . Each graph has a histogram of the data 301 and a Rician distributionfitted 302 to the histogram. The number of histogram bins were chosenautomatically by the Matlab function histogram, and the function histfitwas used to plot both the histogram and the distribution.

Referring now to FIG. 5 and FIG. 6 , FIG. 29 illustrates thedistributions of OS-scheme of FIG. 1 correlator outputs for an additivewhite gaussian noise (AWGN) channel of the datasets of FIG. 3 and FIG. 4, and FIG. 30 illustrates the distributions of OS-scheme of FIG. 1correlator outputs for a Multipath communications channel for thedatasets of FIG. 3 and FIG. 4 . The distributions for all datasets havebeen included in FIG. 5 and FIG. 6 , which illustrate magnitude andphase distributions of the 16OS-scheme correlator outputs for the AWGNand Multipath channels. Note that the bins are narrower for theincorrect data because the incorrect data sub-sets contain M−1=15 timesmore samples than the correct data sub-sets.

There is an overlap of correlator values between the correct andincorrect distributions for the MP_−7.5 dB dataset, as shown in FIG. 3and FIG. 4 . Values of the correct distribution starts from around ‘15’,which happens to be far in the middle of the incorrect distribution—nearwhere the mode lies. Also, the incorrect distribution ends in values ataround ‘55’, that is in the middle—and close to its mode—of the correctdistribution. Overlaps between the correct and incorrect distributionsmeans it is likely that the correct correlator output value is close to,and may be smaller than, the incorrect correlator output values in thesame received set of M=16 codes.

By looking at the distributions for other SNRs (illustrated in FIG. 5and FIG. 6 ) it can be seen that not all SNRs exhibit overlaps betweencorrect and incorrect distributions. Since the incorrect correlatorshave always their minimum values near zero, the incorrect distributionshave bins starting from values close to zero, regardless of what the SNRis. However, as the SNR goes down from 0 dB, the maximum output valuesof the incorrect correlators in the distribution increase. Hence,smaller SNRs will have a greater range of incorrect correlator outputvalues. Also, in the correct correlator distributions as the SNR goesdown the minimum values decrease, and the maximum values increase. Inother words, smaller SNRs will have a greater range of correctcorrelator values, too, but from both small and large sides of thedistribution. Therefore, the smaller the SNR the more chance there willbe overlap between values of the correct and incorrect correlatoroutputs. This confirms the concept that with smaller SNRs, choosing thecorrect code index becomes more difficult.

Thus, in some examples of the invention, a representation of the twoaggregated correlator distributions method 202 is proposed, wherein thefirst and second aggregated correlator output magnitude distributionsare each represented by a set of distribution parameters. For example,in some instances, the set of distribution parameters may comprise anon-centrality parameter s and a scale parameter a 303 of FIG. 3 .

Estimation Methods

The analysis of the later-described OS-PSK Soft Demapping and EXIT Chartimplementation assumes a testbench environment, in which prior knowledgeof the true values of the transmitted bits 107 and OS symbols 115 ofFIG. 1 is available. In practical known receivers, this knowledge willnot be available and the distribution parameters s and σ 111 must beestimated in its absence. In order to obtain the distribution parameters111 of correlator output values, online or offline approaches (asillustrated at 4403 in FIG. 35 ) can be taken. In an online approach, areceiver data analyser circuit 116 is responsible for analysing thecorrelator outputs from the demodulator 118 received at run-time,finding the best distribution to fit to the data, and calculatingparameters of the distributions, with the benefits from real-time tuningof distribution parameters.

Offline Approaches

In an offline approach, such as shown in FIG. 1 and FIG. 35 , thecorrelator distributions may be calculated offline and used to build alibrary of correlator distributions on all applicable modulation-channelcombinations. For example, the six datasets mentioned earlier in thisdocument can be used as models for different channel conditions andmodulation schemes. A configuration-time switch 117 can be configured tochoose the right set of data based on the system's modulation scheme andchannel type. In some examples, this could be performed as an extensionof any other channel estimation tasks performed by the demodulator 118.For example, the outputs of these channel estimation tasks could be usedto index a look-up table of pre-computed correlator outputdistributions. More specifically, an offline estimation of correlatordistributions may be used to record correlator outputs for severalchannel conditions and used to build a library, say in a form of alook-up table (LUT) 112, of those distributions. Then, during actualdata transmissions, an offline channel estimation method 4405 identifiesthe current state of the channel and chooses the correspondingdistribution from the look-up table 112.

Another offline approach example would be to use a single set ofcorrelator distributions in all cases, irrespective of the varyingchannel conditions. This single set of correlator distributions could berecorded during a worst-case scenario, perhaps at the lowest SNR, wherereliable synchronisation can be achieved. When the channel conditionsmatch this worst-case scenario, the use of the corresponding correlatordistributions will ensure the best possible performance. When thechannel conditions are better than this worst-case scenario, the chanceof decoding success can be expected to increase, even though the assumedcorrelator distributions are pessimistic compared to the truedistributions.

Online Approaches

Referring now to FIG. 35 , and as an alternative to using datasets toestimate the distributions offline, online example methods 4407 4408 aredescribed, which calculate the distribution parameters in the earlystages of a real data transmission flow 4400, such as when a channelestimation task is in progress. The first online channel estimationmethod 4407 is through correlating received synchronisation signals withknown synchronisation signals. Let's take an example: suppose that forthe transmission of 4-bit messages (k=4) the demodulator 118 knows thatbefore transmitting data, the transmitter sends a synchronisationsequence of ‘0000’, ‘0001’, . . . , ‘1111’, which has M=16 messages andcorrespond to symbol values 0 to M−1=15, respectively. Therefore, thedemodulator 118 expects that, amongst the M=16 correlators, thecorrelator with index ‘0’ should, in the first received transmission,output the highest cross-correlation magnitude. In the same way,correlator with index ‘1’ is expected to output the highest magnitude inthe second transmission, and so on until the last symbol is transmitted.

Using the first online channel estimation method 4407, as the receiver102 is aware of the true symbol values, it can associate every set ofM=16 correlator outputs of a transmission to its symbol value. Thesynchronisation sequence can be transmitted a few times, so that foreach symbol value there will be a number of M=16 correlator output sets,(in the same manner as illustrated in FIG. 26 , but with a differenttime order), and hence distributions can be estimated based on arequired sample size. This online technique is sometimes referred toherein as the correlator distribution estimation using synchronisationsequences of the first online channel estimation method 4407. With thisfirst online channel estimation method 4407, the maximum distributionsapproach 201 of FIG. 2 can be used to obtain 2^(2k) distributions, orthe two aggregated distributions approach 202 may be employed to obtainthe two correct 205 and incorrect 206 aggregated correlatordistributions, as shown in FIG. 2 . It is also generally possible to usea number of distributions between 2 and maximum 2^(2k) values, which isexplained in an example later. Following distribution aggregation, adistribution fitting method (such as the histfit function of Matlab) maybe used to estimate the s and σ parameters 303 of FIG. 3 for eachaggregated distribution.

FIG. 35 also identifies a second online technique that can operateconcurrent to the data transmissions, referred to as thelargest-magnitude correlator distribution estimation of the secondonline channel estimation method 4408. In this second online channelestimation method 4408, an assumption is made that the correlator withthe largest output magnitude, in normal channel conditions, correspondsto transmitted message value. As any correlator in any transmission isoutputting either the largest magnitude or not the largest one,recording the values for each of the two cases for all the receivedtransmissions 4402 under consideration provides two distributions forany correlator: the distribution when that correlator provides theoutput with the largest magnitude and the distribution when thatcorrelator provides an output that does not have the largest magnitude.This is shown in the middle columns 3601 of FIG. 27 , which illustratesthe correlator output distributions of the largest-magnitude method.

Referring now to FIG. 31 , a correlator output distribution 3600 of alargest-magnitude method, according to some example embodiments of theinvention.

There is a total of M*2=32 distributions of largest and non-largestcorrelator output magnitudes, shown in the middle columns 3601 of FIG.27 . As illustrated, the number of distributions here is between 2 andthe maximum 2^(2k). As shown, it is also possible to aggregate 3603 allthe largest-magnitude distributions (M=16 of them) and aggregate 3604all the non-largest-magnitude distributions (also M=16 of them), eachset into a separate distribution producing two distributions, as shownin the right-hand column 3602 in FIG. 27 . Again, following distributionaggregation, a distribution fitting method (in some examples such as thehistfit function of Matlab) may be used to estimate the s and σparameters for each aggregated distribution. It is then assumed that thes and σ parameters of the aggregated largest-magnitude distributionprovides a reasonable estimate of the corresponding parameters 303 ofFIG. 3 of the aggregated correct distribution. Likewise, it may beassumed that the s and σ parameters of the aggregatednot-largest-magnitude distribution provides a reasonable estimate of thecorresponding parameters 303 of FIG. 3 of the aggregated incorrectdistribution.

Note that the largest-magnitude correlator distribution estimationapproach in the second online channel estimation method 4408 of FIG. 35could be further refined by completing a first estimation of the s and σparameters, then using these to calculate LLRs as detailed in the‘calculating symbol LLRs’ section below, before they are provided to achannel decoder 104 in FIG. 1 . In some examples, the channel decoder104 of FIG. 1 can then attempt to remove any errors in the LLR sequenceand use, say, a Cyclic Redundancy Check (CRC) to determine if it hasbeen successful. If not, then the channel decoder 104 can providefeedback LLRs to the Data Analyser circuit 116 of FIG. 1 . These LLRscan then be considered and, in some instances, may cause theclassification of the correlator outputs between the largest-magnitudeand not-largest-magnitude groups to be overridden. More specifically, acorrelator output having the largest magnitude for a particulartransmission may be swapped for another that does not have the largestmagnitude, when forming the largest-magnitude group, if the feedbackLLRs provide a sufficiently strong suggestion that the magnitudes do notreflect the correct transmission.

In summary, three methods to estimate the correlator output magnitudedistributions have been described with respect to FIG. 35 :

-   -   the offline channel estimation method 4405, of using correlator        datasets 112, with a) 2^(2k) (max.), and b) 2 (min.), number of        distributions;    -   the online method of using synchronisation sequences of the        first online channel estimation method 4407, with a) 2^(2k)        (max.), and b) 2 (min.), number of distributions; and    -   the online method of largest-magnitude correlator outputs of the        second online channel estimation method 4408, with a) 2M, and b)        2, number of distributions

In each of the above three methods, the approach using two distributionscomprises of a first aggregated distribution of all the correlatoroutput magnitudes where, each correlator output, in its transmission, is‘assumed’ to correspond to its transmitted signal, amongst all the Mcorrelator outputs of the same transmission. Likewise, there is a secondaggregated distribution of all the correlator output magnitudes where,each correlator output, in its transmission, is ‘assumed’ not tocorrespond to its transmitted signal. In other words, regardless ofwhich of the above three methods is used, the two aggregateddistributions in each method, are assumed to refer to the same two setsof correlator outputs across all three methods.

To explain the above approaches in a different way, the M correlatoroutputs of any one transmission may be divided into the following twogroups. The first group comprises of the single correlator output thatcorresponds to one of the M possible signals that is selected as thetransmission signal. The second group comprises of the M−1 correlatoroutputs that correspond to the M−1 possible signals, where none isselected as the transmission signal. Assuming several transmissions takeplace, the magnitudes of the first group of aggregated correlatoroutputs for several transmissions can be represented by a singledistribution which is referred to as the first aggregated correlatoroutput magnitude distribution. In the same way, the second aggregatedcorrelator output magnitude distribution represents the second group ofaggregated correlators for several transmissions. Therefore, using anyof the three methods of distribution estimation listed above, theapproach with two distributions refers to the first and the secondaggregated correlator output magnitude distributions.

In investigations carried out by the inventors and as detailed below,the correlator distributions of the offline channel estimation method4405 are measured from the available datasets and stored in look uptables 112, in order to minimise the effect of estimation error.Furthermore, the two aggregated distribution approach (of the two firstand second aggregated distributions) is adopted due to its generality,as compared to other approaches with more distributions, and itsrobustness to varying channel conditions.

In summary, methods have been described for estimating the parameters ofthe first and second aggregated correlator output magnitudedistributions, wherein at least one of the following is employed:

the first set of distribution parameters of the first aggregatedcorrelator output magnitude distribution are estimated in the firstonline channel estimation method 4407 of FIG. 35 by fitting a firstprobability distribution to the magnitudes of correlator outputsobtained by correlating received synchronisation signals with knownsynchronisation signals;

the first set of distribution parameters of the second aggregatedcorrelator output magnitude distribution are estimated in the firstonline channel estimation method 4407 of FIG. 35 by fitting a secondprobability distribution to the magnitudes of correlator outputsobtained by correlating received synchronisation signals with signalsother than the known synchronisation signal;

the first set of distribution parameters of the first aggregatedcorrelator output magnitude distribution are estimated in the secondonline channel estimation method 4408 of FIG. 35 by fitting a thirdprobability distribution to the magnitudes of correlator outputs havingthe greatest magnitude among sets of 2^(k) correlator outputs obtainedby the bank of 2^(k) correlators;

the first set of distribution parameters of the second aggregatedcorrelator output magnitude distribution are estimated in the secondonline channel estimation method 4408 of FIG. 35 by fitting a fourthprobability distribution to the magnitudes of the 2^(k)−1 correlatoroutputs that do not have the greatest magnitude among sets of 2^(k)correlator outputs obtained by the bank of 2^(k) correlators;

the first set of distribution parameters of the first and secondaggregated correlator output magnitude distributions are selected in theoffline channel estimation method 4405 of FIG. 35 from a look-up-table112 of FIG. 1 .

In examples of the invention, it has also been demonstrated that thefirst, second, third or fourth probability distributions may berepresented using the Rician distribution.

Calculating OS LLRs

Logarithmic Likelihood Ratios (LLRs) are a form of soft decision, whichexpress not only what the most likely value of an uncertain decision is,but also how likely this value is. LLRs can have any real value and areoften used to represent likelihood of bits in having values of zero orone. When bits are represented by zeros and ones, they are referred toas ‘hard bits’, and if they are represented using LLRs they are known as‘soft bits’, and those LLRs are referred to as ‘bit LLRs’. However, itis known that LLRs can also be used to represent analogue signal valuesor symbols, as opposed to digital bits. In such a case, those LLRs maybe referred to as symbol LLRs and the signals represented by the symbolLLRs may be known as ‘soft signals’, as opposed to ‘hard signals’ whenthe analogue signal values are used without forming into anotherrepresentation. More specifically, if there are M number of possiblevalues for a symbol, then the associated probabilities may be expressedusing a set of M LLRs, where each LLR compares the probability of aparticular value having occurred, against the probability that thatvalue did not occur.

The inventors of the present invention developed a Matlab function thattakes correlator output magnitudes as the set of inputs to the softdemapper circuit and turns them, using the correlator outputdistributions, into symbol LLRs (which sometimes may be referred to assoft magnitudes) as the set of apriori soft signals, as shown by Convertto OS LLRs demapper circuit 113 in FIG. 1 . Therefore, it can be saidthat the output magnitudes 109 of the 2^(k) correlators in FIG. 1 arecombined with the s and σ parameters 111 of the first and secondaggregated correlator output magnitude distributions in order to obtainthe set of apriori soft signals 110 comprising 2^(k) soft magnitudes.Note that if non-Rician distributions were adopted to model theaggregated output magnitude distributions, then the correspondingparameters 111 may be used in this LLR calculation operation instead.The following discussion uses the case where k=4 and M=16 as an example.However, it is envisaged that the concepts described herein can beextended readily to other values.

In FIG. 1 , the demapper circuit 113 arranged to convert the correlatoroutputs to OS symbol LLRs takes at a time M=16 correlator outputmagnitudes 109 (both correct and incorrect) of one received symbol andreturns M=16 corresponding symbol LLR values as soft signals 110, andperforms this for all received 4402 symbols of a frame. Each of theseM=16 symbol LLRs correspond to the same received symbol (i.e., a 4-bitmessage, k=4) and they collectively demonstrate a probabilisticrepresentation of the 4-bit message. Later in the receiver 102, theConvert to Bit LLRs circuit 119 turns the M=16 symbol LLRs or softsignals 110 of the original 4-bit message into k=4 bit LLRs, as the setof extrinsic soft bits 103, where each bit LLR corresponds to one bit ofthe 4-bit message. In summary, each transmitted symbol 115 leads to thegeneration of a set of M=16 symbol LLRs or soft signals 110 in thereceiver, which are then converted to a set of k=4 bit LLRs, or softbits 103.

Hereafter, the description will first focus on the operation of thedemapper circuit 113 arranged to convert the correlator outputs to OSsymbol LLRs, which outputs M=16 OS LLRs or soft signals 110 pertransmitted symbol 115. The description will then focus on the operationof Convert to Bit LLRs circuit 119 of FIG. 1 , which outputs k=4 bitLLRs, or soft bits 103 per transmitted symbol.

The developed Matlab function, which implements the conversion to OSsymbol LLRs 4410 of FIG. 35 , instead of accepting just 16 correlatorvalues, returns symbol LLRs for any number of M correlator values fed toit as a vector, as in step 4409 of FIG. 35 . In some examples, thisfunction takes the following values as inputs: the vector of thecorrelator values, the modulation parameter M (M=16 in this work),non-centrality and scale parameters of the two correct and incorrectdistributions (s_(corr), σ_(corr), s_(incorr), σ_(incorr)). The functionalso outputs the same number of symbol LLRs as the length of inputcorrelator vector.

Referring now to FIG. 32 , graphs 700 illustrate a conversion to OSsymbol LLRs for the AWGN channel for the OS-scheme datasets of FIG. 5 .Concurrently, referring also to FIG. 33 , graphs 800 illustrate aconversion to OS symbol LLRs for a Multipath communications channel forthe OS-scheme datasets of FIG. 6 . Graphs 700 illustrate the symbol LLRAWGN values 701 datasets and graphs 800 illustrate the symbol LLRMultipath values 701 datasets provided by the developed Matlab functionacross an entire range of correlator output values; from zero to themaximum (that is the maximum value of the correct correlator outputs).In a similar manner to the correlator output distributions, the range ofcorrelator output values increases as SNR goes down. For example, forthe AWGN channel while the minimum correlator output value is zero forall SNRs, the maximum correlator output values increase from near 70 forthe 0 dB-SNR dataset to near 100 for the −7.5 dB-SNR dataset. Asexpected, the functions represented by the symbol LLR plots are allstrictly increasing. This is expected as there should not be an LLRvalue for more than one correlator output value. The range of symbolLLRs, from both positive and negative ends, decrease as SNR goes down.This is expected as the certainty of signals to represent certain values(shown by the correlator outputs) must decrease as the power of noiseincreases with respect to the signal power, and this is captured by theprobabilistic nature of the LLR values.

The definition and derivation of the symbol LLRs is as follows:

$\begin{matrix}{{{symbol}{LLR}}\overset{\bigtriangleup}{=}{\ln\left\lbrack \frac{\Pr\left( {{correct}❘{{correlator}{output}}} \right)}{\Pr\left( {{incorrect}❘{{correlator}{output}}} \right)} \right\rbrack}} & \lbrack 1\rbrack\end{matrix}$

Applying Bayes theorem gives

$\begin{matrix}{{{symbol}{LLR}} = {\ln\left\lbrack \frac{{\Pr\left( {{{correlator}{output}}❘{correct}} \right)} \times {\Pr({correct})}}{{\Pr\left( {{{correlator}{output}}❘{incorrect}} \right)} \times {\Pr({incorrect})}} \right\rbrack}} & \lbrack 2\rbrack\end{matrix}$

Here, the conditional probabilities are characterised by the Riciandistribution, resulting in: Pr (correct)=1/M and Pr (incorrect)=(M−1)/M.Making these substitutions gives

$\begin{matrix}{{{symbol}{LLR}} = {\ln\left\lbrack \frac{{RicianPDF}\left( {{{correlator}{output}},s_{correct},\sigma_{correct}} \right)}{{{RicianPDF}\left( {{{correlator}{output}},s_{incorrect},\sigma_{incorrect}} \right)} \times \left( {M - 1} \right)} \right\rbrack}} & \lbrack 3\rbrack\end{matrix}$

In summary, a method for OS demodulation 118 has been described, whereinthe output magnitudes 109 of the 2^(k) correlators of FIG. 1 arecombined with the first set of distribution parameters 111 of the firstand second aggregated correlator output magnitude distributions in orderto obtain a set of apriori soft signals 110 comprising 2^(k) softmagnitudes, as in step 4410 of FIG. 35 .

In accordance with a second aspect of the invention, an exampleimplementation of the Convert to Bit LLRs circuit 119 of FIG. 1 . isdescribed, to explain how the two conversion functions may be evaluated.

Conversion to Bit LLRs and EXIT Chart Evaluation: OS Scheme

Referring now to FIG. 9 , a top-level block diagram of an alternativeOS-scheme transmission system 900 adapted according to exampleembodiments of the present invention is illustrated. For testingpurposes, the alternative OS-scheme transmission system 900 wasdeveloped in Matlab to perform, in the receiver chain 901, softdemapping of the output magnitudes 109 of a demodulator's 118correlators into extrinsic bit LLRs 904 is performed in the softdemapper circuit 907, giving compatibility with the iterative decodingprinciple. A testbench (again developed in Matlab) evaluates thefunctionality of the new soft demapping function by measuring thequality of the extrinsic bit LLRs, and presents the quality results inthe form of extrinsic information transfer (EXIT) charts.

In this example, the Convert to Bit LLRs circuit 906 is developed toprovide compatibility with an iterative decoding setup alongside thedemapper circuit 113, arranged to convert the correlator outputs to OSsymbol LLRs, in order to build the soft demapper circuit 907 or softdemapping functionality.

Iterative Decoding Principle

Again, each set of M=16 OS LLRs from a total of N/4×16 OS symbol LLRs(k=4) 908 generated by the demapper circuit 113 and corresponds to one4-bit message. Given that k=4 bit LLRs is sought for each 4-bit message(one bit LLR per message bit), each set of M=16 OS LLRs needs to beconverted into a set of k=4 bit LLRs. Therefore, a total of N bit LLRs909 may be obtained from N/4×16 OS LLRs from the Convert to Bit LLRscircuit 906, as shown in FIG. 9 . While this conversion by default canbe performed without using feedback from the decoder—when the feedbackbit LLRs 910 in FIG. 9 are removed or hard-wired to provide zero-valuedLLRs—the conversion can also benefit (as in step 4418 of FIG. 35 ) fromthe feedback bit LLRs 910, according to the principles of iterativedecoding. In this example, M=16 is used, although the inventorsrecognise and appreciate that the concepts and definitions hereindescribed can be applied to any value of M=2^(k).

Use (as in step 4418 of FIG. 35 ) of feedback during the conversion (asin step 4413 of FIG. 35 ) to bit LLRs usually happens after the decoder912 has failed 4421 the cyclic redundancy check (CRC) in the CRC decoder911 at the end 4416 of its decode process. The decoder 912, in such acase, instead of asking for a hybrid automatic repeat request (HARQ)retransmission from the transmitter 913, may want to try a furtherattempt of symbol-bit LLR conversion in the Convert to Bit LLRs circuit906 with the hope that the use (as in step 4418 of FIG. 35 ) of feedbackbit LLRs 910 may cause the decode to pass 4422 in a subsequent attempt,and hence time, bandwidth and power is saved with respect to aretransmission. The Convert to Bit LLRs circuit 906, or simply the BitLLRs circuit, stores 4411 the N/4×16 OS LLRs in a memory unit until theiterative decoding process is concluded 4422, whereupon it clears thememory. After a second round of OS-symbol-to-bit LLR conversion, if thedecoder 912 fails 4421 CRC in the CRC decoder 911 again, it may stillwant to try more conversion attempts 4421. This is because furtheriterations of demap-decode uses (as in step 4418 of FIG. 35 ) a feedbackvalue that is based on a history of past LLRs, and hence it is morelikely that the decoder 912 will pass 4422. If the CRC decoder 911 keepsfailing 4421, eventually the decoder 912 may decide to ask for aretransmission (HARQ 4422) from the transmitter 913, or even abort thecurrent code circuit, instead of another 4421 iteration of demap-decode.This process of going through multiple iterations of decoding 912 andconversion in the Convert to Bit LLRs circuit 906 (as in step 4413 ofFIG. 35 ) of symbol to bit LLRs (in the soft demapper circuit 907) isknown as the iterative decoding principle or the turbo principle [1].

Terminology: Types of LLRs

While the generation of one set of N bit LLRs may go through severaliterations of demap-decode (due to consecutive CRC failures 4421),generation of another set(s) of bit LLRs may pass 4422 CRC in the firstround and need no iteration. In any round of demap-decode, either thefirst round with no feedback (as in step 4412 of FIG. 35 ), or theproceeding rounds (as in step 4421 of FIG. 35 ) with feedback (as instep 4418 of FIG. 35 ), the values on signals between the decodercircuit 912 and soft demapper circuit 907 can be classified into threetypes: apriori LLRs, extrinsic LLRs, and aposteriori LLRs. Apriori LLRsare always inputs and contain pre-existing information with respect tothe circuit they are fed into. Extrinsic LLRs are always outputs andcontain new information based on the calculation performed in thecircuit they are generated from. Aposteriori LLRs are also outputs butare representative of all information (including both the pre-existingand new information) from the first iteration and for all symbols forthe same code.

Decoder cores 915 with soft output typically generate aposterioriinformation in the form of aposteriori LLRs 914 as outputs. This couldbe in the form of using internal memory to update their state of themessage information over time, hence collecting all information. Itcould also be that what decoders receive as input are themselvesrepresentative of all information, and hence so the decoder's output inthe form of aposteriori LLRs 914. Although the decoders typically outputaposteriori LLRs, as shown 914 in FIG. 9 , the type of data exchangedbetween the decoder 912 and the soft demapper circuit 907 is extrinsicLLRs. If this were not the case, and the two circuit interchangedaposteriori data, there would have been positive feedback causing thedata to diverge and become corrupt [1].

One example of how the three different types of LLRs flow between thedecoder 912 and the soft demapper circuit 907 is shown in FIG. 9 andalso explained with respect to FIG. 35 . Assume that a new code isreceived 4402 at the receiver chain 901: code A. As in step 4409 of FIG.35 , the demodulator 118 has generated a set of N/4×16 correlator outputmagnitudes 109 of code A, and at step 4410 of FIG. 35 the same number ofOS LLRs is output from the demapper circuit 113 that is arranged toconvert the correlator outputs to OS symbol LLRs. The Convert to BitLLRs circuit 906 receives these OS symbol LLRs 908 as apriori data andconverts (as in step 4413 of FIG. 35 ) them into N bit LLRs 909. TheConvert to Bit LLRs circuit 906 also stores 4411 a copy of the OS LLRsin its internal memory, to reuse (as in step 4419 of FIG. 35 ) them incase iterative decoding 4421 is applied. At this time (represented bystep 4412 of FIG. 35 ), the feedback bit LLRs 910 contains no LLRs (orequivalently carries N zero-valued LLRs) as this is the first time thatdata corresponding to code A is processed in the soft demapper circuit907. Generally, in some examples of the invention, the Convert to BitLLRs circuit 906 generates its output based on both the received N/4×16OS symbol LLRs 908 and the N feedback bit LLRs 910 received from thefeedback line. Given that the feedback bit LLRs 910 are representativeof pre-existing data—even though zero-valued (as in step 4412 of FIG. 35) in the first iteration—the output of the Bit LLR circuit 906 will be Nbit LLRs 909 of the aposteriori type.

Since the decoder 912 provides feedback bit LLRs 910, and there is aclosed-loop flow of data between the decoder 912 and the soft demappercircuit 907, the decoder 912 expects extrinsic type of input LLRs aspart its processing, as opposed to aposteriori LLRs, which would createa positive feedback loop [1]. Therefore, the soft demapper circuit 907,which is setup in the closed loop with the decoder 912, subtracts thefeedback N apriori bit LLRs 910 from the N aposteriori bit LLRs 909output of the Convert to Bit LLRs circuit 906 to generate N extrinsicbit LLRs 904, as in step 4414 of FIG. 35 . As mentioned, the firstiteration (as in step 4412 of FIG. 35 ) of the Convert to Bit LLRscircuit 906 for code A, will have zero-valued apriori bit LLRs for thefeedback bit LLRs 910, and hence the extrinsic bit LLRs 904 output fromthe soft demapper circuit 907 will be equal to the output of the Convertto Bit LLRs circuit 906 in the first iteration. The demapper's extrinsicbit LLRs 904 output from the soft demapper circuit 907 is de-interleaved(π⁻¹) in the decoder 912 and is fed into the decoder core 915subsequently as N apriori bit LLRs 916 of the apriori type for thedecoder 912. Following this, the decoder 912 can use these apriori LLRs916 to generate a vector of decoded bits 917, which are then fed to theCRC decoder 911 shown in FIG. 9 . If the CRC decoder 911 check passes4422, then the transmission process is completed successfully.

In FIG. 35 , if the decoder 912 fails 4421 due to CRC decoding 911 forcode A and decides to apply iterative decoding, the decoder 912 cangenerate a sequence of N feedback bit LLRs 910. The result, for examplethe LLR feedback output in the form of aposteriori LLRs 914 of thedecoder core 915 will be aposteriori, and for the same reason explainedearlier to avoid positive feedback in the closed loop with the softdemapper circuit 907, the decoder 912 subtracts the input apriori bitLLRs 916 from decoder core's 915 aposteriori LLR feedback output 914.The resulting sequence of N extrinsic LLRs 918 are interleaved (π) andfed back (as in step 4418 of FIG. 35 ) to the soft demapper circuit 907as apriori feedback bit LLRs 910 through the feedback line, which willpossibly have non-zero values this time. The Convert to Bit LLRs circuit906 then uses the feedback bit LLRs 910 for a second OS-symbol-to-bitLLR conversion (as in step 4413 of FIG. 35 ) for code A, when it alsouses (as in step 4419 of FIG. 35 ) the code A's OS LLRs that it hadstored 4411 in its memory from the previous iteration. The Convert toBit LLRs circuit 906 will still keep the same OS LLRs in its memory, asthe CRC decoder 911 may fail 4421 for a second time and a thirdOS-symbol-to-bit LLR conversion (as in step 4413 of FIG. 35 ) may berequired. The end of the iterative decoding is decided by the decoder912, which may occur 4422 due to, either a CRC pass (resulting in asuccessful transmission process), or reaching a maximum number ofdecoding iterations (whereupon the transmission process is abandoned anddeemed unsuccessful). Following the processing of code A, the next blockof code (code ‘B’), may have been received 4402 in the receiver chain901, and the above process will be repeated for code B.

Calculating Bit LLRs

In the earlier description of conversion to bit LLRs for an OS scheme,it was explained how OS symbol LLRs 908 are generated from thecorrelator output values. where, it is explained how bit LLRs 909 arecalculated (as in step 4413 of FIG. 35 ) from the apriori OS symbol LLRs908 and the fed-back apriori bit LLRs 910 in an iterative decodingapproach.

No Feedback from the Decoder

First, in a scenario where there is no feedback bit LLRs 910 from thedecoder, or equivalently, the apriori feedback bit LLRs 910 to the softdemapper circuit 907 have values of zero, a 4-bit message m exists forwhich k=4 bit LLRs need to be found; one bit LLR for each of the messagebits. In some examples, the 4-bit message can have any value from theset of 4-bit binary combinations {0000, 0001, . . . , 1111} 3701, asshown in FIG. 28 , which illustrates 4-bit message combinations andcorresponding OS symbol LLR parameters. The following parameters mayalso be used to represent the bit LLRs of the message: LLR₃ ^(bit,out),LLR₂ ^(bit,out), LLR₁ ^(bit,out), LLR₀ ^(bit,out) which correspond inthe same order from the most significant bit (MSB) to the leastsignificant bit (LSB) of the message. For inputs to the Convert to BitLLRs circuit 906, there is M=16 OS symbol LLRs values, where each valuecorresponds to one of the M=16 message combinations 3702. The OS symbolLLRs 3703 are represented using the parameters LLR₀ ^(sym,in), LLR₂^(sym,in), . . . , LLR₁₅ ^(sym,in), as listed in FIG. 28 . Therefore, onone side there exists M=16 OS symbol LLR values corresponding to M=16message combinations, and on the other side the M=16 symbol LLRs are tobe used to obtain k=4 bit LLRs for the 4-bit message.

Calculation

Referring now to FIG. 29 , terms in a bit LLR calculation areillustrated, when there is no feedback from a decoder, according to someexample embodiments of the invention. Here, the calculation (as in step4413 of FIG. 35 ) of the bit LLRs is better understood using an example.If it is assumed that LLR_(i) ^(sym)=LLR_(i) ^(sym,in) for all i in therange [0,M−1] or [0,15]. If bit 0 (LSB) of the transmitted message was a“1”, like messages “0001” or “1011”, it may be expected that thedemodulator 118 will express a collective probability of all the messagecombinations with their LSB equal to “1” (column 8 in FIG. 29 ) that isrelatively higher than the collective probability of the messagecombinations with their LSB equal to “0” (column 7 in FIG. 29 ), whenthe channel conditions are favourable. In the same way, if bit 1 of themessage had a value of “1”, like “0010” or “1111”, it may be expectedthat the demodulator 118 will express a collective probability of allthe message combinations with their bit 1 equal to “1” (see column 6 inFIG. 29 ) that is higher than those with their bit 1 equal to “0” (seecolumn 5 in FIG. 29 ). The same can be said for the cases when messagebits were “0”. The decoder is not aware of the actual values of themessage bits, but attempting to determine them by considering combiningprobabilities (represented in LLRs) in a way that leads to a finalmessage combination that is most likely amongst all to be the actualmessage. The left-hand side columns 3801 of FIG. 29 show the differentmessage combinations for the 4-bit message (k=4). The right-hand sidecolumns 3802 show how each of the M=16 symbol LLRs relate in the bit LLRcalculation (as in step 4413 of FIG. 35 ) for each bit of the 4-bitmessage.

In order to calculate (as in step 4413 of FIG. 35 ) the bit LLR valuefor one bit, the M=16 symbol LLRs is first divided into two groups of 8LLRs each, according to FIG. 29 . For each bit of the 4-bit message(with an index in the range [0,k−1] or [0,3]), there are M/2=8 messagecombinations where the same bit index has a value “1”, and M/2=8combinations where the same bit index has a value “0”. For example, forbit 3 (MSB) of the 4-bit message, message combinations {0000, 0001, . .. , 0111} has their MSB equal to “0”, and message combinations {1000,1001, . . . , 1111} has their MSB equal to “1”. The LLR valuescorresponding to the first and second sets of 8 message combinations ofthe message's MSB are therefore {LLR₀ ^(sym), LLR₁ ^(sym), . . . , LLR₇^(sym)} and {LLR₈ ^(sym), LLR₉ ^(sym), . . . , LLR₁₅ ^(sym)}, and areshown in columns 1 and 2 of FIG. 29 , respectively. It is also knownthat the logarithmic-likelihood ratio is defined as:

$\begin{matrix}{{{LLR}\overset{\bigtriangleup}{=}{\ln\left\lbrack \frac{\Pr\left( {{bit} = 0} \right)}{\Pr\left( {{bit} = 1} \right)} \right\rbrack}},} & \lbrack 4\rbrack\end{matrix}$

and that multiplications and divisions in the probability domaincorrespond to additions and subtractions in the LLR domain,respectively. Therefore, the bit LLR value, for instance for bit 3, willbe the LLR probability of bit 3 when it is “1” subtracted from LLRprobability of bit 3 when it is “0”, that is LLR₃ ^(bit,out)=L₃^(bit,0)−L₃ ^(bit,1), as shown 3803 in FIG. 29 .

In order to calculate each of the parameters L₃ ^(bit,0), L₃ ^(bit,1),L₂ ^(bit,2) . . . , in the bottom row 3804 of FIG. 29 , thecorresponding LLR values need to be combined, which will be LLRparameters in column 1 for L₃ ^(bit,0) as an instance. To obtain theprobability of the event that any message combination amongst a givenset of combinations occurs, the probabilities of all combinations withinthe given set must be added. This is because the message combinationsare mutually exclusive—only one message combination is the actual valueof a 4-bit message. For instance, the probability that the message isone of the values {“0000”, “0101”, “1010”} is Pr[“0000” U “0101” U“1010”]=Pr[“0000”]+Pr[“0101”]+Pr[“1010”].

The addition of probabilities can be approximated using the Jacobianlogarithm in the LLR domain. The Jacobian logarithm is:

log(a+b)=max(log(a),log(b))+log(1+e ^(−|log(a)-log(b)|)),   [5]

and assuming a and b are mutually-exclusive probabilities, they can becombined using their LLR values by writing log(a+b)=max(LLR_(a),LLR_(b))+. This operation is called the 36axstar operation, and the sign

is used to denote it. The addition of probabilities can be representedusing the 36axstar operator in the LLR domain. For instance, L₃ ^(bit,0)is defined as L₃ ^(bit,0) LLR₀ ^(sym)

LLR₁ ^(sym)

. . .

LLR₇ ^(sym), which contains the terms in column 1 of FIG. 29 . In thesame way, other parameters L₃ ^(bit,1), L₂ ^(bit,0), . . . can becalculated from their corresponding columns in FIG. 29 .

With Feedback from the Decoder

As explained previously, for every 4-bit message (k=4) there are k=4apriori feedback bit LLRs 910 fed back from the decoder 912 to theConvert to Bit LLRs circuit 906, as shown in FIG. 9 . The followingparameters are used to represent the apriori soft bits 910 (feedback bitLLRs), LLR₃ ^(bit,in), LLR₂ ^(bit,in), LLR₁ ^(bit,in), LLR₀ ^(bit,in),which correspond, in order, to MSB down to LSB of the message.

Given that the soft demapper circuit 907 is now receiving multipleinputs, they can be enumerated according to the following:

-   -   the M output magnitudes of the correlators referred to as the        first set of inputs to the soft demapper circuit 907. These are        used to generate a first set of apriori soft signals comprising        M OS symbol LLRs 908;    -   the second set of inputs to the soft demapper circuit 907 may be        defined to be a second set of apriori soft signals comprising        the k feedback bit LLRs 910 (or k soft bits).

Now the question is how these k=4 new values of soft bits or feedbackbit LLRs 910 can be used, along with the previous M=16 OS symbol LLRs908, to improve the k=4 feedback bit LLRs 909 as the output of theConvert to Bit LLRs circuit 906. In FIG. 28 , it was shown that each ofthe M=16 OS symbol LLRs 908 represent a probability corresponding toone, out of M=16, of the message combinations shown in the left-handside columns 3801 of FIG. 29 . However, in this scenario, what is therelation of the k=4 apriori feedback bit LLRs 910 with respect to eachmessage combination? In some examples, it is known that a positive LLRmeans the bit is more likely a “0”, and a negative LLR means it is morelikely a “1”. Now, if the actual message was “0001”, it may be expectedthat the apriori LLRs corresponding to bits 1-3 were positive, and theLLR value corresponding to bit 0 was negative. Therefore, the value LLR₃^(bit,in)+LLR₂ ^(bit,in)+LLR₁ ^(bit,in)−LLR₃ ^(bit,in) may be expectedto be positive for the message “0001”. In the same way, it can be saidthat if the message, for instance, was “1010”, it may be expected thatthe following is positive: −LLR₃ ^(bit,in)+LLR₂ ^(bit,in)−LLR₁^(bit,in)+LLR₀ ^(bit,in). This explanation can hold for all M=16 messagecombinations: if a message combination is the actual received message,its corresponding apriori bit LLR combination is expected to bepositive. FIG. 30 illustrates 4-bit message combinations, withcorresponding OS symbol LLR parameters and apriori bit LLR combinations.The apriori bit LLR combinations 3901 are listed and the division by 2in each combination is required for the calculation (as in step 4413 ofFIG. 35 ) of output bit LLRs.

The above explanation can be taken further by saying that if a messagecombination is the actual message, its corresponding apriori bit LLRcombination is expected to have the largest value amongst all other bitLLR combinations 3901. Therefore, by calculating the M=16 apriori bitLLR combinations of the left-hand side columns 3801 of FIG. 29 and FIG.30 , the largest of which directs the decoder to the message combinationwhere according to the k=4 bit LLRs has the highest chance of being theactual message.

So far, in some examples and for the M=16 message combinations of theleft-hand side columns 3801 of FIG. 29 and FIG. 30 , there are two setsof M=16 soft signals that demonstrate the likelihood of the messagecombinations to represent the actual 4-bit message; the symbol LLRs 3703and the apriori bit LLR combinations 3901, as shown in FIG. 30 . As bothsets are in LLR representation, they can be added together to become asingle set of LLRs corresponding to the message combinations. Therefore,if the symbol LLR parameters in FIG. 30 are defined to be LLR_(i)^(sym)=LLR_(i) ^(sym,in)+LLR_(i) ^(sym,bit) for all i in the range[0,M−1] or [0,15], the bit LLRs generated by the Convert to Bit LLRscircuit 906 can then be calculated using the methodology explained forFIG. 29 . The resulting (as in step 4413 of FIG. 35 ) bit LLRs 909 areaposteriori LLRs, as they represent all information, including both thenewly received OS symbol LLRs 908 from the upstream and the old apriorifeedback bit LLRs 910 received from the decoder 912.

Summary

In summary, the demapper circuit 113 and Convert to Bit LLRs circuit 906have been described that are arranged to convert the correlator outputsto OS symbol LLRs and for generating (as in step 4413 of FIG. 35 )aposteriori soft bit LLRs 909, wherein a second set of apriori softsignals comprising k soft bits 910 are provided as a second set ofinputs to the circuit. Furthermore, the circuit combines all apriorisoft signals to generate a set of 2^(k) aposteriori soft signals andwherein the set of 2^(k) aposteriori soft signals are combined to obtainthe set of aposteriori soft bit LLRs 909. Finally, the aposteriori softbit LLRs 909 are combined with the soft bits or feedback bit LLRs 910 ofthe second set of apriori soft signals, in order to obtain a set ofextrinsic bit LLRs 904 comprising k soft bits, as in step 4414 of FIG.35 .

The flow 4400 of the soft demapper for the OS scheme, as demonstrated inthe flowchart of FIG. 35 , may be summarised as follows. Initially at4401, the demapper receives 4402 a set of signals as the outputs of thedemodulator that correspond to a transmitted frame. Then, in someexamples, it is decided which of the three different methods ofestimating the distributions of the correlator outputs, are to beemployed. If the offline method is chosen 4423, the characteristics ofthe channel, such as the signal-to-noise ratio and channel type (e.g.,AWGN), are identified in the offline channel estimation method 4405. Theresult of the identification is then used to address a pre-computedtable, say pre-computed table 112 of FIG. 1 , of distribution parametersof the correlator output magnitudes. If, in contrast, an online methodof distribution estimation is chosen at 4424, the choice will be eitherthe use of synchronisation sequences in the first online channelestimation method 4407, or applying the largest magnitude method of thesecond online channel estimation method 4408. Whichever estimationmethod is employed, the estimated parameters of the magnitudedistributions, alongside the collected correlator output magnitudes ofstep 4409 of FIG. 35 , are used to calculate the OS soft signals of step4410 of FIG. 35 , which may be in the form of LLRs, as describedpreviously in the section that calculates OS LLRs.

Following that, the calculated 4410 OS soft signals are stored 4411 ininternal memory, in case a demap-decode round of iterative decoding isrequired later. In a first iteration of a possible iterative decodingprocess, there is no value on the feedback path from the decoder. Hence,this feedback will be all zero-valued, as in step 4412 of FIG. 35 .Next, the aposteriori soft bits, in the form of LLRs (the OS bit LLRs),are calculated, as in step 4413 of FIG. 35 . This is followed byconverting (as in step 4414 of FIG. 35 ) the aposteriori soft bits intoextrinsic sift bits as the type required by, and sent (4415) to, thedecoder. After the decoder is finished with the process of decoding theextrinsic information that it received, the demapper receives (4416) theCRC status and the decoded soft bits from the decoder. Following a checkof the CRC status at 4417, if the check failed 4421, turbo decoding maybe applied in some examples of the invention and the received 4416decoded soft bits may be treated (as in step 4419 of FIG. 35 ) asapriori information fed back from the downstream decoder. Also, the OSsoft signals, which had been calculated 4410 previously, are loaded (asin step 4418 of FIG. 35 ) from memory as another set of aprioriinformation for the calculation of soft bits. The symbol-bit LLRconversion uses all apriori information to make a second calculation4413 of soft bits as bit LLRs. The demap-decode iterations of turbodecoding are ended 4422 either by a CRC pass or by abandoning furtherdecoding operations of the current frame, which may lead into, forexample, a hybrid automatic repeat request (HARQ) re-transmission. Atthis point, the demapping of the current frame is ended at 4420.

Testbench

Previously a method of providing the decoder 912 with extrinsic bit LLRs904 of the received message, for example in the form of soft bits, hasbeen described, by converting 4413 OS symbol LLRs 908 to bit LLRs 909using the iterative decoding principle. Here, an evaluation of theconversion to extrinsic bit LLRs 904 is described. Different approachescan be used to evaluate the result of the Convert to Bit LLRs circuit906—which is also the extrinsic bit LLRs 904 output of the soft demappercircuit 907. One approach is to observe the bit error rate (BER) whenusing the soft decision demapping, and have it compared against the BERof the same transmission but with a hard demapping of correlator outputvalues into hard bits instead of LLRs. Other approaches characterise thegenerated extrinsic bit LLRs 904 from the soft demapper circuit 907,such as measuring mutual information (MI) histogram and measuring mutualinformation averaging, which is described later.

It is noted that, as some of the above approaches rely on comparisons ofthe decoded bits 919 against transmitted bits 920, they are onlyapplicable in lab-environment testbenches where transmitted bits 920 areaccessible, as opposed to real systems where only received 4402 data 921are in hand. Examples of these lab-only evaluation methods are BER andMI histogram measurements. However, although these methods are onlyapplicable to lab environments, they provide a good measure inevaluating the quality of the extrinsic bit LLRs 904 output of the softdemapper circuit 907.

High-Level Operation

A testbench was developed in Matlab to measure the quality of theextrinsic bit LLRs 904 output from the soft demapper circuit 907 when ituses the above-described conversion to bit LLRs. A block diagram of thetestbench 1000 for the 16OS scheme (orthogonal signalling with M=16, andthe datasets taken from [5]) is illustrated in FIG. 10 . As shown, thereare no encoders or decoders: instead, encoded bits 1001 are simulatedusing random bits from a uniformly distributed random number source1002. Also, the data that is meant to be fed into a decoder in realsystems, is generated from the soft demapper circuit 907, and goesthrough a few measurements (such as BER 1005 and MI calculations 1006,1007). The results of the measurements are used by a final processingfunction 1008, which plots an EXIT chart. In FIG. 10 , the blocks andflows in the set 113, 114, 906, 907, 1001, 1004, 1013, 1020, 1023, 1024,1026, 1031, 1032 and 1035 correspond to parts of the testbench that arein common with a real transmitter-receiver communication system 900. Theremaining blocks and flows are only specific to the lab testbench andare typically absent from real systems.

Every execution of the testbench is based on the choice of a truechannel and an estimated channel and generates one EXIT chart 1011. In apractical system, it may not be possible for the receiver chain 901 toperfectly estimate the channel characteristics. This is represented inthe testbench of FIG. 10 by using a first channel model (referred to asthe true channel model 1009) to simulate the transmission and by using asecond (potentially different) model 1010 to provide the channelcharacteristics that are obtained by the (potentially imperfect) channelestimator. Indeed, in some applications, channel estimation may beentirely absent from the receiver chain 901 and a fixed set of(worst-case) channel characteristics may be assumed, irrespective ofwhat the true channel characteristics are. The user of the testbenchwill choose the two channel models as inputs 1009, 1010, as shown in theright-hand side in FIG. 10 , and will expect the output EXIT chart 1011that is specific to the two chosen channels, as shown in the left of theblock diagram. The testbench 1000 was applied to several true andestimated channel combinations, with their EXIT charts illustrated inFIG. 12 to FIG. 14 . In these figures, each EXIT chart has the same trueand estimated channel types, but sometimes different SNRs. The true andestimated channels in each EXIT chart are both based on either theadditive white Gaussian noise (AWGN) model, or the multipath (MP) model.While FIG. 12 has a different SNR between its true and estimatedchannels, FIG. 13 and FIG. 14 have the same SNRs each. FIG. 11 is anexample EXIT chart when both true and estimated channels are based onthe AWGN_-7.5 dB dataset.

Mutual Information

EXIT charts demonstrate a characterisation of the unit that they weregenerated from, which could be a demapper, or a decoder. In examplesdescribed herein that seek the evaluation of a soft demapping model, allEXIT charts 1100, 1200, 1300, 1400 illustrated in FIGS. 11-14 belong tosoft demapper circuit 907. In these charts, the X axis is the mutualinformation of the apriori bit LLRs 1013: which is a measure of thequality of the feedback (which would come from the channel decoder in areal system, but which comes from a Generate random LLRs circuit 1014 inthe testbench 1000) and fed into the Convert to Bit LLRs circuit 906.The mutual information between two random variables quantifies theamount of information in one variable that can be obtained by observingthe other variable, and MI values are in the range [0,1]. An MI value ofMI=0 means that there is no feedback from the decoder, and the feedbackline will comprise a sequence of N zero-valued bit LLRs. Any value ofMI>0 corresponds to cases when feedback from the decoder is present, andlarger values of MI mean the feedback values have greater quality. The Yaxis in the EXIT charts 1100, 1200, 1300, 1400 illustrated in FIGS.11-14 , is also a quality measure between zero and one, and correspondsto the output value generated by the soft demapper. In each of theseEXIT charts 1100, 1200, 1300, 1400 in this document, there are threeplots 1101, 1102, 1103 and one point shown by a cross 1104, and somenumber figures 1105 on the maximum coding rate achievable for the softdecision approach.

Testbench Flow

To generate the EXIT chart data, the testbench loops over a number oftest indices 1016, where each 1017 corresponds, in the EXIT chart 1011,to points in all plots with the same MI value 1018 for the apriori bitLLRs 1013. For each test index 1017 of the test indices 1016, an aprioriMI value 1018 is chosen. The system is simulated using this MI value1018, demapper output of N extrinsic bit LLRs 1004 quality parameters(such as BER 1005) are measured, and eventually some points in the EXITchart 1011 are identified. For example, the execution of the testbenchwith MI=0.3, produces one point for each of plot 1101, plot 1102 andplot 1103 in the EXIT chart 1100 in FIG. 11 .

Transmitter

In each simulation with a test index 1017, encoded bits 1001 aregenerated from a uniformly-distributed random number source 1002 and fedinto the bits to symbol circuit 114, which converts bits into symbolsbased on a modulation with 16 symbols (M=16). Hence, for N encoded bits1001 there will be N/4 symbols (k=4) 1020 to be modulated.

Datasets

The models used in this testbench for different modulation schemes andchannel types are represented by the datasets that were included in theprevious correlator distribution investigation and conversion to symbolLLRs for an OS scheme, with the addition of one extra dataset. Thesedatasets are provided by [5] and are 30 presented using the followingnotations: AWGN_100 dB, AWGN_0 dB, AWGN_−3 dB, AWGN_−7.5 dB, MP_0 dB,MP_−3 dB, MP_−7.5 dB. Each of these datasets is a large matrix of 8100rows, where each row contains (a) a symbol value 3502 in the range[0,M−1] or [0,15], and (b) M=16 correlator output magnitudes 3503, whichwere generated for that symbol value from the mathematical model of thecorresponding modulation scheme and the channel. A memory 1012 in FIG.10 stores and replicates all the above datasets, with in this examplethere being seven datasets in total.

Models of True and Estimated Channels

In this example, the choice of the true channel 1009 will select one ofthe available seven datasets and treat that as the modulation-channelsimulation model 1021 of the testbench 1000. During the testbenchsimulation, for every symbol value generated from the Bits to Symbolscircuit 114 of FIG. 1 , a row with the same symbol value from the ChosenModulation & Channel Model 1022 of FIG. 10 is randomly chosen and thecorresponding 16 correlator values in the same row are output 1023. Inthis way, the correlation between the correlator outputs is preserved.Note however that the memory in the channel between successivetransmissions is not modelled by this approach. However, this isjustified because the proposed soft decision demodulator does notexploit this memory and because the spreading sequences used in [5] aredesigned to mitigate the dispersion that causes this memory. The useralso needs to choose the estimated channel. In this example, the DataAnalyser circuit 1024 of FIG. 10 fits Rician distributions to all rowsfrom the user-chosen 1010 estimated dataset 1025 and returns fourparameters 1026 corresponding to the distributions of the correct andincorrect sets of correlator data, as defined and explained in theprevious correlator distribution investigation and conversion to symbolLLRs for an OS scheme. While in this testbench 1000, the channelestimation task of the Data Analyser circuit 1024 is performedconcurrent to the simulation, in real systems it could take place onlineby analysing the received signal, or it could take place offline usingvery large sets of channel data if a fixed set of channelcharacteristics is to be assumed. Performing channel estimation offlinecan avoid large on-line complexity overheads.

Hard Decision Flow

In the testbench 1000 a hard decision flow 1027 of the receiver 1028 wasincluded in order to calculate its BER 1029 and compare it against theBER performance 1030 of a soft decision bit LLR model. The Hard Decisionfor Symbols circuit 1031 receives M=16 correlator values from thechannel model and performs a hard decision by taking the index 1034 ofthe largest correlator value as the 4-bit message value (k=4), whichthen passes the index to the Convert to Bits circuit 1032 to generatethe equivalent bits 1035. For instance, if the largest correlator valueamongst the M=16 has an index of ‘9’, the result of a hard demappercircuit 1033 for this symbol will be “1001”. When the hard demappercircuit 1033 demapped all symbols into bits, the BER measurement circuit1036 compares those bits with the true encoded bits 1001 from thetransmitter chain 1037 and calculates the BER value using the formulaBER=number of bits in error divided by the number of all bits. The BERvalue 1029 will be a fractional number in the range [0,1]. While smallerBERs represent better performance, the value 1-BER is plotted in theEXIT chart (using a cross point “X”) so that it can be compared againstother quality measures, whose larger values also demonstrate betterperformance, and similarly have values between zero and one. The harddecision flow 1027 is independent from the soft decision flow 1038 andits iterative feedback, and for every dataset there will be just onehard BER value 1029 1104. Also, since the hard decision flow 1027 doesnot use feedback, its BER 1029 can be compared against the case in thesoft decision flow when there is no feedback. Due to this, the harddecision BER point is plotted 1104 at apriori MI=0 in the EXIT charts,as shown in FIG. 11 .

Quality of LLRs

The soft decision flow 1038 is based on receiving apriori bit LLRs 1013as feedback to the soft demapper circuit 907, as shown in FIG. 10 .Instead of using a decoder model in the testbench, it is sufficient forthe purpose of the testbench that the apriori bit LLRs 1013 to the softdemapper circuit 907 are generated differently from a decoder, which inthis case are generated by the Generate random LLRs circuit 1014. Inorder to simulate a real receiver, the generated apriori bit LLRs 1013must be, with a certain quality, similar to the encoded bits 1001, andhence the Generate random LLRs circuit 1014 takes as input the trueencoded bits 1001 in order to create LLRs with such a similarity. Theserandom LLRs are generated according to a Gaussian distribution, asdescribed in FIG. 4 of [1].

Feedback Apriori Bit LLRs: A Function of MI in this Testbench

The quality of the feedback apriori bit LLRs 1013 in the testbench 1000of FIG. 10 are represented by the MI value as the mutual information.The MI is a statistical measure that can be used to represent how muchthe demodulated extrinsic LLRs (or feedback apriori bit LLRs 1013) haveshared information with respect to the true encoded bits 1001.Therefore, as a statistical measure it can be expected that the MI valueis generally calculated to find out the dependence between the encodedand demodulated bits, for example, in lab-environment testbenches wheredecoder models are present. However, in this example testbench 1000,since feedback apriori bit LLRs 1013 are not generated from a decodermodel, but as a function of the true encoded bits 1001, the MI of theencoded and demodulated bits may be defined for different test indices.An MI value 1018 will become an input to the Generate random LLRscircuit 1014 to generate mimicked decoded bits. The Generate random LLRscircuit 1014 contains a mathematical function that produces LLRs whosemutual information with respect to the given input bits is equal to theinput MI value. The Generate MI value circuit 1039 uses a test index1017 to generate an MI value 1018 in the range [0,1].

Soft BER Calculation: Why Aposteriori Data?

Calculating the bit error rate in the soft decision flow 1038 requiresaposteriori information from the soft demapper-decoder interface. Thisis because, the output of a soft decoder is typically aposteriori data(as explained previously in the section describing a conversion to bitLLRs and exit chart evaluation for an OS scheme) and hence theaposteriori information would be the closest form to that of a decoder'soutput. Obtaining aposteriori data from the decoder-demapper interfaceis shown in FIG. 10 with the summation 1040 of the N extrinsic bit LLRs1004 and N apriori bit LLRs 1013 from and to the soft demapper circuit907, respectively. The testbench 1000 then makes a hard decision 1041 onthe aposteriori bit LLRs 1042 to provide N bits 1043 from the Naposteriori bit LLRs 1042. Here, a hard decision of binary ‘0’ is madefor positive aposteriori LLRs and a hard decision of ‘1’ is used fornegative LLRs. The resulting N bits 1043 are compared in terms of BER1005 against the true N encoded bits 1001 from the transmitter chain1037 in order to provide a BER measure 1030 for the test index 1017 andthe MI 1018 of that execution.

Comparison of Soft and Hard BER Values

The comparison of the soft BER value when MI=0 against the hard BER 1029is valid as both values are calculated based on bits resulting from thesame type of (extrinsic) data from their demapping of symbols to bits.This is obvious with the hard decision flow 1027, as there is nofeedback in this flow, and hence the data from the hard demapper circuit1033 is extrinsic. Also, since the soft decision flow 1038 when MI=0 hasits feedback apriori bit LLRs 1013 with values of zero, the aposterioribit LLRs 1042, in this case, are equal to the N extrinsic bit LLRs 1004generated from the soft demapper circuit 907, as shown in FIG. 10 .Therefore, a decrease in BER value from the hard decision flow 1027 tothe soft flow 1038 means that the use of LLRs has been able to increasethe quality of the receiver by reducing the error rate. In the EXITchart, this BER performance increase will be the case if the cross point1104 of the hard BER value happens to be underneath the plot 1101 of thesoft decision BER value—as the plot values are in the form of 1-BER.Generating soft decision BER values also shows the effect of increasingthe quality of feedback LLRs on the BER performance. For example, FIG.11 demonstrates that using the example soft demapping approach, thequality of LLRs to the decoder increases as the quality of the feedbackLLRs enhances. It may be observed that the soft (decision) demappercircuit 907 produces an equal or better BER than the hard (decision)demapper circuit 1033 in all cases shown in FIG. 12 to FIG. 14 .

MI: Histogram and Averaging Methods

There are two other quality measures that can characterise a softdemapper circuit's output: the mutual information histogram 1102 and themutual information averaging 1103, as demonstrated in the EXIT charts.Both measures provide mutual information, and both look at the output Nextrinsic bit LLRs 1004 of the soft demapper circuit 907 to calculatetheir MI, as opposed to the BER measure that required aposteriori bitLLRs 1042. The histogram method (equation (2) in [1]) provides themutual information 1044 between the N extrinsic bit LLRs 1004 and thetrue encoded bits 1001 from the transmitter chain 1037. This knownmethod does not assume that ‘LLR values could not be wrong’—i.e., thisknown method does not trust LLRs—and checks those LLRs against the trueencoded bits 1001. In contrast, the averaging method (the equationimmediately below FIG. 4 in [1]) solely looks at the N extrinsic bitLLRs 1004 and provides a measure 1045 of quality without an outsidereference. Thus, it provides a quality measure based on trusting LLRs.For this reason, the averaging method works best when the decodingalgorithms are optimal.

Upper Bounds on Achievable Coding Rates

The MI histogram method can also be used to provide an upper bound onthe achievable coding rate when the soft demapper circuit characterisedby the MI histogram is used. The achievable coding rate between adecoder and a demodulator in general (which includes a demapper) ismainly dependent on the following two aspects. The first aspect is howwell the decoder and the demapper are matched (see discussion of the‘area gap’ in [1] for more details). Like demappers, the behaviour of adecoder can also be characterised using EXIT charts. One can compare ademapper's EXIT chart with that of a decoder to determine how the twomatch. The second aspect in identifying the achievable coding rate isthe block length applied when using the system: shorter block lengthsdecrease the coding rate required in practice (see [1] for moredetails).

Regardless of whether a decoder's EXIT chart is present, or a codelength is chosen, the demapper's EXIT chart contains figures that definethe theoretical upper bound on the coding rate that supports reliablelow-BER operation using the demapper. This upper bound differs betweenthe cases when there is iterative feedback in 1107 and when there is noiterative feedback in 1106 in FIG. 11 . For example, according to theEXIT chart of FIG. 11 , the apriori MI histogram value for when thefeedback quality has an MI of zero is 0.87 (rounded towards zero). Thismeans that the maximum achievable coding rate using the example softdecision demapping approach without an iterative feedback for anAWGN_7.5 dB channel is 0.87, shown at 1106. In the presence of iterativefeedback (when feedback has MI>0), the area below the MI histogram plotwill be the maximum achievable coding rate [1]. In FIG. 11, the areabelow the MI histogram plot is 0.92 (rounded towards zero), and hencethe maximum achievable coding rate in the example soft decisiondemapping approach when there is iterative feedback for an AWGN_7.5 dBchannel is 0.92, shown at 1107.

Results: EXIT Charts High-SNR Charts

The EXIT charts in FIG. 12 to FIG. 14 show that for SNRs ≥−3 dB in allchannels (5 charts in total) there is not any bit error: all hard andsoft BER values are zero. Also, the MI quality measures of thedemapper's extrinsic LLRs, both histogram and averaging methods, havevalues of 100% for all MI values of the feedback quality. This verifiesthe soft decision demapping model according to example embodiments ofthe invention for normal high-SNR conditions: the model successfullyprovides bit LLRs to the decoder with 100% mutual information with thetrue bits sent from the transmitter, and with zero bit error rates.

Low-SNR Charts Without Iterative Feedback: BER

The EXIT charts for small SNRs of −7.5 dB (for example the two charts intotal 1301, 1401 in FIG. 13 and FIG. 14 ) also demonstrate that the softdecision demapping 25 model according to example embodiments of theinvention works as expected. The two EXIT charts of AWGN 1301 and MP1401 channels in FIG. 13 and FIG. 14 , each with an SNR value of −7.5dB, have 1-BER values of 0.97 (rounded towards infinity) for their harddecision, and have slightly better values for their soft decision whenthere is no iterative feedback. This means that the soft demapping model30 according to example embodiments of the invention managed to preservethe bit error rate when switching from the hard model to the soft modelwithout feedback.

With Iterative Feedback: Effect of Feedback MI on BER and the Two MIFigures

The two low-SNR EXIT charts 1301, 1401 in FIG. 13 and FIG. 14 alsodemonstrate that as the quality of feedback LLRs increases (when MI>0),the quality of the demapper circuit's output LLRs, as well as the biterror rate improve. The 1-BER figure approaches to 100% values when thefeedback quality MI goes to the value of 1, as may be expected for thecase where perfect information is fed back. Also, the demapper circuit'soutput quality MI figures of histogram and averaging methods, start fromvalues between 85%-90% for feedback MI=0, and become approximately equalto 97% when the feedback MI is ‘1’. The two MI figures have also valuesclose to each other for all feedback MI values, which means that the twoMI measures represent the quality of the feedback LLRs confidently andshow that the consistency condition of [1] is met.

Maximum Achievable Coding Rates

Depending on the decoder and the chosen block length, a receiver may beable to converge to parts of its demapper circuit's EXIT charts that hasthe highest quality values. In the illustrated EXIT charts, the factthat highest BER performance and MI quality values are both near97%-100% when the feedback MI is equal to 1, means that the proposeddemapper circuit approach according to example embodiments of theinvention may provide the highest quality LLRs. The low-SNR EXIT charts1301, 1401, of FIG. 13 and FIG. 14 also show that the upper bound on thecoding rates are 0.88 and 0.93 (rounded to nearest 2^(nd) decimalplace), for the cases when the iterative feedback is absent and ispresent, respectively.

OS-PSK Soft Demapping and EXIT Chart Evaluation

In this section, a proposed soft-decision approach in demapping of ademodulator's correlator outputs from an orthogonalsignalling-phase-shift keying (OS-PSK) modulation scheme into extrinsicsoft bits in the form of logarithmic likelihood ratios (LLRs)—also knownas bit LLRs or soft bits is described, according to some examples of theinvention. The operation of one example of the proposed soft demapper isdemonstrated in the flowchart of FIG. 36 .

The previous section presented a soft demapping approach for OS-onlycorrelator outputs. The functionality of some circuits in FIG. 15 hasbeen previously described with regard to earlier figures, so will not berepeated in order not to obfuscate the concepts described here. FIG. 15introduces the following additional circuits: a Convert to PSK symbolLLRs circuit 1501 and a Symbol-to-symbol LLR circuit 1502. This sectionalso explains how, in the transmission systems captured in FIG. 15 , thetransmitter chain 1503 applies the direct-sequence spread spectrum(DSSS) technique (using the Spreading Sequence Generator circuit) andthe modulator circuit 1504 to convert information bits into OS-PSKmodulated data.

Modulation Model Transmitter Chain

The OS-PSK modulation scheme, as shown in FIG. 15 , turns the N encodedbits 1505 into a number of OS symbols 1506 and PSK symbols 1507according to the work done by [7]. Take the example when the OS schemehas a modulation parameter (referred to as the OS radix) of M=16 (alsoreferred to as the 16OS scheme), which corresponds to k=log 2M or 4 bitsper OS symbol. Likewise, consider the case where the PSK modulationparameter (referred to as the PSK bits-per-symbol) has a value ofQ_(m)=2, which corresponds to a PSK radix (also known as modulationorder) of 2^(Qm)=4. A PSK scheme with Q_(m)=2 is also called thequadrature PSK (QPSK). In every k+Q_(m)=4+2=6 bits of an encodedmessage, in this example, 4 bits are turned into an OS symbol and 2 bitsare converted into a PSK symbol, where both symbols have complex values.Assuming N is an exact multiple of 6, there will be a total ofN/(k+Q_(m)) or N/6 OS symbols 1506 and the same number of PSK symbols1507. In the transmitter chain 1503, the OS-mapped k bits are referredto as the first set of bits 1508 and the PSK-encoded Q_(m) bits arereferred to as the second set of bits 1509.

Note that in this section, in accordance with some examples of theinvention, a fixed OS radix of M=16, but with a variable PSK radix, isemployed. This approach enabled the inventors to explore the impact ofvarying the PSK radix. However, it is envisaged that, in other exampleembodiments, the soft-demapping methodology and concepts describedherein can be applied to an arbitrary number of OS bits ‘k’.

Indeed, in the extreme, a skilled practitioner could envisage a schemewhere the OS radix is M=1 and there are k=0 bits conveyed by theselection of a spreading sequence, and with all N=Q_(m) bits beingconveyed by the phase of the spreading sequence. In this scheme, thetransmitter would repeatedly transmit the same spreading sequence, eachtime with a phase rotation that conveys Q_(m) bits.

Direct-Sequence Spread Spectrum

In order to improve the signal to noise ratio (SNR) at the receiverchain 1510, the DSSS technique is used in the transmitter chain 1503which multiplies 1517 the OS symbols 1506 by a pseudorandom basesequence of signals represented by complex numbers. The base sequence iscalled the spreading sequence, and each signal value in the spreadingsequence 1511 is known as a chip. The chips have shorter durationscompared to the encoded bits 1505, and hence have larger bandwidths. Theconversion of the information bits into chips has the effect ofscrambling the information bits and widening their frequency spectrum,and hence reducing the overall signal interference when the signals aremodulated. The receiver chain 1510 is aware of the spreading sequenceand uses it to de-spread the received signal.

Modulation

In the example above, while k=4 bits 1508 amongst 6 bits of the encodedbits 1505 that are turned into an OS symbol 1506 and then turned into aspreading sequence 1511 of complex values, the other Q_(m)=2 PSK-encodedbits 1509 are mapped 1515 into one (amongst four) possible complex PSKsymbols 1507 in a quadrature PSK scheme. The four possible QPSK-mappedvalues have different phases, but the same magnitude, and are equallyspaced in a complex plane. The PSK-symbol 1507 of the Q_(m)=2 PSKencoded bits 1509 is multiplied, in the Modulator circuit 1504, by eachvalue in the spreading sequence 1511. The result is a sequence 1518 ofcomplex values, that is a rotated version of the spreading sequence 1511corresponding to the k=4 OS-encoded bits 1508, where the amount ofrotation is according to the value of the other Q_(m)=2 PSK-encoded bits1509. This final sequence 1518 of complex numbers contains theinformation for all the k+Q_(m)=6 encoded bits 1505 and is transmittedthrough the antenna(s).

Data

The receiver chain 1510 will demodulate the signals based on itsknowledge of the applied schemes, such as the PSK modulation order (fromthe value of Q_(m)) and the spreading sequence 1511. The datasets usedin this work to evaluate the example soft demapping approach areprovided in [6], and are based on a 16OS-QPSK scheme (that is with M=16,Q_(m)=2), and were generated based on a spreading sequence with 50chips. Subsequent sections propose a technique that allows these16OS-QPSK datasets to be generalised and used to model any PSK radix.These datasets belong to the same set of channels and SNR values usedpreviously: AWGN_100 dB, AWGN_0 dB, AWGN_−3 dB, AWGN_-7.5 dB, MP_0 dB,MP_−3 dB, MP_−7.5 dB. The AWGN and MP terms refer to the additive whiteGaussian noise and the multipath channels, respectively. For example,FIG. 31 illustrates the AWGN_0 db dataset of the 16OS-QPSK scheme [6]:the table shows the first 20 rows out of 8100. Each dataset is comprisedof 8100 rows, where each row includes the value 4001 of one 6 bits ofthe message and the corresponding M=16 pairs 4002 of in-phase (I) andquadrature-phase (Q) correlator values.

Magnitudes of Correlator I-Q Pairs

The I and Q values in each I-Q pair represent the real and imaginaryparts of a complex correlator output value, respectively. For instance,in row 1 of FIG. 31 , the first correlator output has a complex value of−0.9-6i, where i is the imaginary unit. The magnitude of an I-Q pairresembles the possibility of the pair's index value, with respect toother pairs amongst the 16 in a row (hence a cross-correlation value,like a correlator's output), to represent 4 bits of the originaltransmitted 6-bit message. Therefore, in a similar manner to thepreviously described example, the one pair amongst M=16 that has thelargest magnitude, is generally expected (in favourable channelconditions) to have its index with a value that is the same as the k=4least significant (LS) bits of the (k+Q_(m)) 6-bit message. Here, theconvention that the PSK bits provide the Q_(m) most significant bits andthe OS bits provide the k least significant bits is adopted. It isenvisaged that other conventions may equally be adopted within theinventive concepts herein described, such as the PSK bits providing thek least significant bits. The I-Q pairs with the largest magnitudes intheir rows are underlined in FIG. 31 . For example, the 9^(th) row 4003in FIG. 31 has its LS k=4 bits of message with a value 7 (‘0111’), andthe index of the largest-magnitude I-Q pair in this row has also a valueof 7. As discussed previously, in one row of a dataset, the I-Q pairwith an index equal to the value of the LS k=4 bits of the message maybe referred to as the “correct” correlator outputs, and the remainingM−1=15 I-Q pairs as the “incorrect” correlator outputs. To elaboratefurther, the ‘correct’ correlator output is provided by the correlatorfor which the corresponding one of the 2^(k) possible signals wasselected as the transmission signal.

Phases of Correlator I-Q Pairs

While the magnitudes of the correlator I-Q pairs contain the informationfor k=4 bits of the (k+Q_(m)) 6-bit message, the phase values of the I-Qpairs represent the information for the remaining Q_(m)=2 bits. Thedatasets have their QPSK modulation on the most significant (MS) 2 bitsof the message. For example, the 2 MS bits of the message in row 1 4004of FIG. 31 is ‘01’, which in this example means this message isQPSK-modulated with a phase indexed as 1 amongst indices in the range[0,3] (that is [0,2^(Qm)-1] in the general case). Depending on the QPSKcoding, phase indices map to a particular set of Gray-coded phasevalues. For instance, with a phase mapping of [π/4, 3π/4, −π/4, −3π/4]to [00, 01, 10, 11], the phase index ‘01’ is mapped to the phase value3π/4, and hence the correct correlator output I-Q pair in row 1 (FIG. 31) is expected to have a phase with value 3π/4.

Hereafter, a technique that allows these 16OS-QPSK datasets to begeneralised and used to model any PSK radix is described. For the sakeof simplicity, in these illustrated examples, phase mappings that beginwith a phase of 0 will be adopted, such as [0, −π] for binary PSK(BPSK), or [0, π/2, −π/2, −90] for QPSK, and so on.

Correlator Output Magnitudes: OS Modulated

Similar to the work in the earlier section that investigated the datafrom an OS-only model, the distributions of the correct and incorrectcorrelator output magnitudes for the OS-PSK scheme can be aggregatedinto two distributions, as the first and the second aggregatedcorrelator output magnitude distributions, respectively. The parameters1520 used to represent each of the two aggregated distributions may alsobe referred to as the first set of distribution parameters. As before,the Rician distribution may be identified as the single distributionwhich fits best to each of both the correct and incorrect sets ofcorrelator output magnitudes. The distributions of correct and incorrectcorrelator output magnitudes, as described previously, are shown in FIG.21 and FIG. 23 , for both the AWGN and the MP channel datasets, and anexample is provided in FIG. 16 for the MP_-7.5 dB dataset. Comparingthese distributions with those of FIG. 5 and FIG. 6 discussed earlierfor the OS-only scheme shows that the data are distributed verysimilarly between the OS-PSK (this section) and the OS-only (earliersection) models. This is demonstrated through the Rician distribution'snon-centrality parameter (s) and scale parameter (σ), which have similarvalues of parameters 303 of FIG. 3 for all SNR values between the twomodels and for the first set of distribution parameters.

In summary, as explained previously, methods for estimating theparameters of the first and second aggregated correlator outputmagnitude distributions have been described, wherein at least one of thefollowing is employed:

-   -   (i) the first set of distribution parameters of the first        aggregated correlator output magnitude distribution are        estimated (as in step 4507 of FIG. 36 ) by fitting a first        probability distribution to the magnitudes of correlator outputs        obtained by correlating received synchronisation signals with        known synchronisation signals; (ii) the first set of        distribution parameters of the second aggregated correlator        output magnitude distribution are estimated (as in step 4507 of        FIG. 36 ) by fitting a second probability distribution to the        magnitudes of correlator outputs obtained by correlating        received synchronisation signals with signals other than the        known synchronisation signal;    -   (iii) the first set of distribution parameters of the first        aggregated correlator output magnitude distribution are        estimated (as in step 4508 of FIG. 36 ) by fitting a third        probability distribution to the magnitudes of correlator outputs        having the greatest magnitude among sets of 2^(k) correlator        outputs obtained by the bank of 2^(k) correlators;    -   (iv) the first set of distribution parameters of the second        aggregated correlator output magnitude distribution are        estimated (as in step 4508 of FIG. 36 ) by fitting a fourth        probability distribution to the magnitudes of the 2^(k)−1        correlator outputs that do not have the greatest magnitude among        sets of 2^(k) correlator outputs obtained by the bank of 2^(k)        correlators;    -   (v) the first set of distribution parameters of the first and        second aggregated correlator output magnitude distributions are        selected (as in step 4505 of FIG. 36 ) from, say, a        look-up-table 1527.

In other examples, it may also be demonstrated that the first, second,third or fourth probability distributions may be represented using theRician distribution.

Correlator Output Phases: PSK Modulated Phase Error Values

The aggregated distributions of the correlator output phase values areshown in FIG. 22 and FIG. 24 for the AWGN 2200 and Multipath 2400channels, and for the correct and incorrect sets of I-Q pairs. The datain these figures are represented in terms of the phase errors: for everyrow in a dataset (like FIG. 31 ), the ‘true’ phase of the transmittedmessage (defined by the Q_(m)=2 MS bits of the message) is subtractedfrom the phase of each correlator I-Q pair as the ‘received’ phases,producing received phase errors. Following this, in some examples, thephase error of the ‘correct’ correlator output was extracted from eachrow of the dataset to obtain the set of ‘correct’ phase errors, whilethe remaining M−1=15 phase errors from each row were pooled into the setof ‘incorrect’ phase errors. FIG. 17 provides histograms and fitteddistributions of the correct phase errors 1701 and incorrect phaseerrors 1702 for the MP_-7.5 dB dataset.

Fitting Distribution to Phase Errors

The parameters of the aggregated correct correlator output phase errordistribution may be referred to as the second set of distributionparameters. The correct phase errors 1701, 1703 were best fitted 1704 tonormal distributions that were constrained to have mean values of zero.This constraint was achieved by fitting the absolute values of thecorrect phase errors to half-normal distributions, so that thedistributions are characterised by just a single spreading parameterσ_(phase) 1705. This is shown in FIG. 15 where the σ_(phase) parameter1723 of the correct phase error distributions is sent to the Convert toPSK symbol LLRs circuit 1501. The incorrect phase errors 1702, as shownin FIG. 22 and FIG. 24 , all have uniform distributions. This means thatthe incorrect phases contain no information and do not need to becharacterised by any distribution parameters.

According to above, only the correct phase errors 1703, and not theincorrect phase errors 1702, will convey information from thecorrelation data. Hence, the distribution of all the correct correlatoroutput phase error values may be referred to as the aggregatedcorrelator output phase distribution. In this name, the term ‘correct’is explicitly excluded, even though the distribution is built from thecorrect set of phase error values. This maintains a generic definitionof the aggregated correlator output phase distribution. As before, thecorrect phase error is provided by the correlator for which thecorresponding one of the 2^(k) possible signals was selected as thetransmission signal.

In summary, an approach has been proposed, wherein the plurality ofaggregated correlator output phase distributions is one, and theaggregated correlator output phase distribution approximates theaggregation of the 2^(k) distributions of the output phases of the 2^(k)correlators when the corresponding one of the 2^(k) possible signals wasselected as the transmission signal. An approach has also been proposedwherein the aggregated correlator output phase distribution isrepresented by a second set of distribution parameters and wherein thesecond set of distribution parameters comprises a spreading parametero-phase.

Estimation Methods

The above analysis assumes a testbench environment, in which priorknowledge of the true values of the transmitted bits 1508 and PSKencoded bits 1509 is available. In practical receivers, however, thisknowledge will not be available and the distribution parameter σ_(phase)1523 must be estimated in its absence. To obtain the distribution ofcorrelator output phases, online (as in step 4524 of FIG. 36 ) oroffline (as in step 4523 of FIG. 36 ) approaches are proposed. In theexample proposed online approaches, a Data Analyser circuit 1524 isresponsible for analysing the correlator outputs 1525 from thedemodulator 1519 received at run-time, finding the best distribution tofit to the data, and calculating parameters 1526 of the distributions,with the benefits from real-time tuning of distribution parameters. Thisis shown in FIG. 15 with the Data Analyser circuit 1524 and is detailedbelow. But first, some offline approaches are discussed, which use thelibrary look up table 1527 of correlator distributions shown in FIG. 15.

Offline Estimation Approaches

As described earlier for the OS-only scheme, in an offline approach, thecorrelator distributions may be calculated offline in order to build alibrary look up table 1527 of distributions on all applicablemodulation-channel combinations. For example, the datasets mentionedearlier can be used as models for different channel conditions andmodulation schemes. A configuration-time switch 1528, as demonstrated inFIG. 15 , can be configured to choose (as in step 4505 of FIG. 36 ) theright set of data based on the system's modulation scheme and channeltype. This could be performed as an extension of any other channelestimation tasks performed by the demodulator 1519. For example, theoutputs of these channel estimation tasks could be used to index (as instep 4505 of FIG. 36 ) a look-up table 1527 of pre-computed correlatoroutput distributions. More specifically, an offline estimation ofcorrelator distributions may be used to record correlator outputs forseveral channel conditions and used to build a look-up table of thosedistributions. Then, during actual data transmissions a channelestimation task identifies (as in step 4505 of FIG. 36 ) the currentstate of the channel and chooses the corresponding distribution from thelook-up table 1527, as shown in FIG. 36 .

Another offline approach option would be to use a single set ofcorrelator distributions in all cases, irrespective of the varyingchannel conditions. This single set of correlator distributions could berecorded during a worst-case scenario, perhaps at the lowest SNR wherereliable synchronisation can be achieved. When the channel conditionsmatch this worst-case scenario, the use of the corresponding correlatordistributions will ensure the best possible performance. When thechannel conditions are better than this worst-case scenario, the chanceof decoding success can be expected to increase, even though the assumedcorrelator distributions are pessimistic compared to the truedistributions.

Online Estimation Approaches

Other than using datasets to estimate the distributions offline, twoonline approaches 4507, 4508 are also proposed which calculate thedistribution parameters in the early stages of a real data transmission,such as when a channel estimation task is in progress. The first onlineapproach of step 4507 in FIG. 36 is through correlating receivedsynchronisation signals with known synchronisation signals. Using thisfirst online approach of step 4507, as the receiver chain 1510 is awareof the true symbol phases, it can associate every set of M=16 correlatoroutputs 1525 of a transmission to its correct phase. This first onlineapproach of step 4507 may be referred to as correlator distributionestimation using synchronisation sequences. Following distributionaggregation in the Data Analyser circuit 1524, a distribution fittingapproach (like the histfit function of Matlab) may be used to estimate(as in step 4507 of FIG. 36 ) the σ_(phase) parameter 1523 for theaggregated distribution. The correlator distribution estimation usingsynchronisation sequences has the advantage of being operated online,but also has its own disadvantages. One disadvantage is thatsynchronisation sequences, unless embedded in time-consuming channelestimations, are usually short sequences. Therefore, they do not alwaysprovide sufficient samples to obtain accurate distributions, which maylower the quality of symbol LLRs 1529 calculated using thosedistribution parameters. Aiming for sufficient accuracy requires longsequences, and that adds a time overhead to the channel estimation phaseand increases power and bandwidth consumption.

The other approach in estimating distribution parameters, that isdescribed earlier for the OS-only scheme, is the online approach of step4508 of FIG. 36 , which considers the largest-magnitude correlatoroutput. The online approach of step 4508 divides the correlator outputs1525 into two groups of a) largest magnitude correlator outputs (eachlargest magnitude would be amongst M outputs of the same receivedmessage), and b) non-largest magnitude correlator outputs (M−1 outputswith non-largest magnitudes of the same received message, and forseveral transmission/messages). In the online approach of step 4508, itis assumed that any largest-magnitude correlator output, amongst the Mcorrelator outputs 1525, corresponds to its transmitted sequence 1518from the transmitter chain 1503. Based on this assumption, the phases ofthe largest-magnitude correlator outputs should also correspond to thephase value of the transmitted sequences 1518, and hence each should berepresentative of the Q_(m) number of PSK encoded bits 1509 in themessage. Therefore, like the offline estimation approach of step 4523where the incorrect phase error values 1702 of the incorrect correlatoroutputs followed a uniform distribution, the phase error values of thenon-largest-magnitude correlator outputs are expected to have a uniformdistribution too. Consequently, the valuable distribution(s) in thelargest-magnitude of step 4508 will be of the phase error values of thelargest-magnitude correlator outputs. These values form the aggregatedcorrelator output phase distribution, as mentioned earlier, but thistime for the largest-magnitude of step 4508. The calculation of thephase errors in the largest-magnitude of step 4508 is the same as thatdescribed earlier, except that the ‘true’ phase value (which was knownin other approaches), is assumed to be the one phase in the phasemapping that is closest to the phase of the largest-magnitude correlatoroutput. More explicitly, the phase error may be estimated as thedifference between the phase of the largest-magnitude correlator outputand the phase mapping that is closest to this.

Note that the largest-magnitude correlator distribution estimationapproach of step 4508 could be further refined by completing a firstestimation of the σ_(phase) parameter 1523 then using these to calculateLLRs, as described later with respect to a soft-demapper circuit, beforethey are provided to a channel decoder 912. The channel decoder 912 canthen attempt to remove any errors in the LLR sequence and use a CyclicRedundancy Check (CRC) decoder 911 to determine if it has beensuccessful. If it has not been successful, then the channel decoder canprovide feedback LLRs to the Data Analyser circuit 1524 of FIG. 15 .These LLRs can then be considered and may cause the classification ofthe correlator outputs between the largest-magnitude andnot-largest-magnitude groups to be overridden. More specifically, acorrelator output having the largest magnitude for a particulartransmission may be swapped for another that does not have the largestmagnitude, when forming the largest-magnitude group, if the feedbackLLRs provide sufficiently-strong suggestion that the magnitudes do notreflect the correct transmission.

A definition for the aggregated correlator output phase distribution isnow provided, which applies to all the estimation approaches asdescribed above. The aggregated correlator output phase distributionapproximates the aggregation of the M distributions of the output phasesof the M correlators when the corresponding one of the M possiblesignals was selected as the transmission signal. The aggregatedcorrelator output phase distribution is represented by the second set ofdistribution parameters.

Summary

In summary, methods for estimating the parameters of the aggregatedcorrelator output phase distribution have been proposed, wherein atleast one of the following is employed:

-   -   the second set of distribution parameters of the aggregated        correlator output phase distribution is estimated (as in step        4507 of FIG. 36 ) by fitting a fifth probability distribution to        the phase errors of correlator outputs obtained by correlating        received synchronisation signals with known synchronisation        signals;    -   the second set of distribution parameters of the aggregated        correlator output phase distribution is estimated (as in step        4508 of FIG. 36 ) by fitting a sixth probability distribution to        the phase errors of correlator outputs having the greatest        magnitude among sets of 2^(k) correlator outputs obtained by the        bank of 2^(k) correlators;    -   the second set of distribution parameters of the aggregated        correlator output phase distribution is selected (as in step        4505 of FIG. 36 ) from a look-up-table 1527.

It has also been demonstrated that the fifth or sixth probabilitydistributions may be represented using the Gaussian distribution.

In the following example embodiment, the soft demapping circuit 1522uses the phases 1530 of the M=16 correlator I-Q pairs to obtain thelogarithmic-likelihood ratio (LLR) representation of the possible phasevalues.

Soft Demapper

Like the soft demapper circuit 907 of FIG. 9 and FIG. 10 , proposedearlier for the OS-only scheme, in this section every message bitrequires an LLR value to feed a soft-decision decoder 912. This meansthat for a (k+Q_(m))-bit message, there needs to be (k+Q_(m)) bit LLRsgenerated by the soft demapping circuit 1522, and hence for a total of Nencoded bits 1505 transmitted there will be N extrinsic bit LLRs 904that the soft demapping circuit 1522 outputs, as shown in FIG. 15 .Since k=4 OS bits of information (out of a (k+Q_(m))-bit message) areconveyed through the correlator output magnitudes 1531 (as describedearlier), feeding those magnitudes, as the first set of inputs to thesoft demapper circuit, to the Convert to OS LLRs circuit 1513 in FIG. 15will provide (as in step 4510 of FIG. 36 ) M=16 OS symbol LLRs 908, asthe first set of apriori soft signals, corresponding to the M=16correlator outputs 1525. Also, as in the OS-only scheme discussedearlier, a set of OS apriori feedback bit LLRs 910 is fed back from thedecoder 912 into the soft demapping circuit 1522 as the second set ofinputs to the soft demapper circuit 1522, wherein those feedback bitLLRs 910 may be referred to as the second set of apriori soft signals.

In this example embodiment, a soft demapping circuit 1522 is describedthat can operate in the generalised case of M-OS-PSK using any number ofPSK bits per symbol Q_(m). However, in the following discussions, QPSKwith Q_(m)=2 will be used frequently as a specific example, in whichcase (k+Q_(m))=6.

Conversion to Bit LLRs

The generation of extrinsic bit LLRs 904 is performed using the Convertto Bit LLRs circuit 1521 (FIG. 15 ). In an example embodiment with nofeedback from the decoder, as described previously, a Convert to BitLLRs circuit 906, was introduced that converted M=16 OS symbol LLRs 908of a 4-bit message to k=4 bit LLRs. The Convert to Bit LLRs circuit 1521in this current section needs to generate k+Q_(m)=6 extrinsic bit LLRs904 for a 6-bit message, comprising of LLRs corresponding to the OSmodulation and LLRs corresponding to the PSK scheme, as describedpreviously with respect to the modulation model. The Convert to Bit LLRscircuit 1521 in this section uses the same approach used by the similarcircuit discussed earlier for the OS-only scheme, but this time it has,as inputs, information on the bits representing the phase of demodulatorcorrelator outputs 1525. This new information is the PSK symbol LLRs1532 provided by the Convert to PSK symbol LLRs circuit 1501, asdemonstrated in FIG. 15 , and it may be referred in some examples as thethird set of apriori soft signals.

Below describes the Symbol-bit LLR circuit 1533 of FIG. 15 , which isresponsible for generating the aposteriori bit LLRs 909. This Symbol-bitLLR circuit 1533 takes input from the Symbol-to-Symbol LLR circuit 1502of FIG. 15 , which is described further below and is responsible forcombining LLR information from inputs provided by three sources, namelythe LLRs of 908, 1532 and 1534. These three sources are the Bit-symbolLLR circuit 1535 (described below, which processes the feedback aprioribit LLRs 910), the ‘Convert to OS LLRs’ circuit 1513 (which processesthe magnitudes 1531 of the correlator outputs) and the Convert to PSKsymbol LLRs circuit 1501 (which processes the phases 1530 of thecorrelator outputs).

Symbol-Bit LLR Circuit

Like the OS-only scheme, it may be assumed that every messagecombination in the OS-PSK scheme has a corresponding symbol LLR. With6-bit messages, this makes a total of 26=64 symbol LLRs for one messagein, for example, the 16OS-QPSK scheme: LLR₆₃ ^(sym), LLR₆₂ ^(sym), . . ., LLR₀ ^(sym). These values are shown in FIG. 15 by the line with theannotation showing the total number of symbol LLRs 1529 for an N-bitencoded bits 1505 as N/(k+Q_(m))×M×2^(Qm) or N/6×16×22 symbol LLRs 1529.The symbol LLRs 1529 are converted (as in step 4513 of FIG. 36 ) to bitLLRs 909 using the Symbol-bit LLR circuit 1533 in FIG. 15 . FIG. 32 isan extension of FIG. 31 , which applied for 4-bit messages, and FIG. 32here illustrates the terms in the symbol-bit LLR conversion for 6-bitmessages.

In FIG. 32 , the values of each of the LLR terms L₅ ^(bit,0), L₅^(bit,1), L₄ ^(bit,0), L₄ ^(bit,1), . . . , L₀ ^(bit,0), L₀ ^(bit,1),are defined by the terms above them in the same column. For example, L₄^(bit,0) in column 4 is defined as L₄ ^(bit,0) LLR₀ ^(sym)

LLR₁ ^(sym)

. . .

LLR₁₅ ^(sym)

LLR₃₂ ^(sym)

LLR₃₃ ^(sym)

. . .

LLR₄₇ ^(sym). The symbol

denotes the maxstar operation that is defined in an earlier section forthe OS-only scheme, where detailed explanation on the calculations ofbit LLRs from symbol LLRs are provided. The bottom row 3804 in FIG. 32defines the values of the aposteriori output bit LLRs, where in thisOS-PSK scheme comprises of two sets of soft bits: the OS bit LLRs (MSQ_(m) LLRs: LLR₅ ^(bit,out) LLR₄ ^(bit,out)) and the PSK bit LLRs (LS kLLRs: LLR₃ ^(bit, out) down to LLR₀ ^(bit,out)). The output OS bit LLRsmay be referred to as the first set of aposteriori soft bits comprisingk soft bits, and the output PSK bit LLRs as the second set ofaposteriori soft bits comprising Q_(m) soft bits.

To obtain (as in step 4514 of FIG. 36 ) the extrinsic bit LLRs 904, asshown in FIG. 15 , the feedback apriori bit LLRs 910 are subtracted fromthe aposteriori bit LLRs 909. This relation with the bits correspondingto OS and PSK schemes separated from each other may be described asfollows. The first set of aposteriori soft bits are combined with thesoft bits of the second set of apriori soft signals, to obtain a firstset of extrinsic soft bits comprising k soft bits. The second set ofaposteriori soft bits are combined with the soft bits of the fourth setof apriori soft signals, to obtain a second set of extrinsic soft bitscomprising Q_(m) soft bits.

Symbol-to-Symbol LLR Circuit

Now the question is how symbol LLRs 1529 are calculated (as in step 4528of FIG. 36 ) using the LLRs coming from the upstream 908, 1532 anddownstream feedback bit LLRs 910. In the OS-only scheme, OS symbol LLRs908 were a function of correlator output magnitudes 109 (as the firstset of inputs to the soft demapper circuit 1522) and feedback OS apriorifeedback bit LLRs 910 (as the second set of inputs to the soft demappercircuit). Here, symbol LLRs are additionally a function of thecorrelator output phases 1530 as the third set of inputs, and feedbackPSK apriori bit LLRs as the fourth set of inputs, to the soft demappingcircuit 1522. The feedback PSK bit LLRs can equivalently be referred to,in some examples, as the fourth set of apriori soft signals.

The Symbol-to-symbol LLR circuit 1502 takes as inputs the following togenerate (as in step 4528 of FIG. 36 ) symbol LLRs 1529: OS symbol LLRs908, PSK symbol LLRs 1532, and symbol LLRs 1534 that are converted (asin step 4527 of FIG. 36 ) from downstream bit LLRs. The latter symbolLLRs 1534 may be referred to as the feedback symbol LLRs (shown in FIG.15 ) which includes both OS and PSK apriori symbol LLRs as the secondand fourth sets of apriori soft signals, respectively. Each of the M=16OS symbol LLRs corresponds to one combination amongst M=16 of the k=4 LSbits of the 6-bit message, and 6 bits can represent 64 combinations.Given that the Q_(m)=2 MS bits of the message can also have fourcombinations by themselves (‘00’, ‘01’, ‘10’, ‘11’), in some examplesFIG. 28 can be extended for the work in this section according to FIG.33 , which illustrates the 6-bit message combinations 4201 andcorresponding LLR parameters 3703, 4202, 4203.

In FIG. 33 , the OS symbol LLRs 3703 have the same values as the symbolLLRs 3703 in the earlier discussion for the OS-only scheme: LLR_(i)^(OS,in) _(OS-PSK)=LLR_(i) ^(sym,in) _(OS-only) for all i in the range[0,M−1] or [0,15]. This is because the work discussed earlier was basedon an OS-only scheme where the cross-correlation data were justmagnitudes, but not phases. As shown in FIG. 33 , the M=16 OS symbol LLRvalues 3703 are repeated after every M=16 combinations. Also, assumethat each message combination (out of 2^(k+Qm)=64) has its own PSKsymbol LLR—it will be explained why this assumption holds and explainhow the PSK symbol LLRs 4202 are calculated in step 4525. Each messagecombination will also have a corresponding feedback symbol LLR 4203 too,as shown in the right-most column in FIG. 33 . The symbol LLR value forevery message combination will be the addition of all LLR terms in thecorresponding row in FIG. 31 . For example, LLR₃₁ ^(sym)=LL/R₁₅^(OS,in)+LLR₃₁ ^(PSK,in)+LLR₃₁ ^(sym,bit). In other words, all apriorisoft signals 908 1532 1534 are combined in the Symbol to Symbol LLRscircuit 1502 to generate in step 4528 a set of 2^(k+Qm) aposteriori softsignals or symbol LLRs 1529, which are combined 1533 in step 4514 toobtain the first set of aposteriori soft bit LLRs 909 and the second setof aposteriori soft bits.

Bit-Symbol LLR Circuit

The feedback bit LLRs 910 in FIG. 15 may contain LLR values fed backfrom the decoder 912 to the soft demapping circuit 1522. If the decoder912 is not feeding back any LLRs, the feedback bit LLRs 910 will have(as in step 4512 of FIG. 36 ) bit LLR values of zero, making nodifference in the computation (as in steps 4527 and 4528) of symbol LLRs1529. Otherwise, the fed back bit LLR values affect (as in steps 4519and 4527) the computation of step 4528 inside the Convert to Bit LLRscircuit 1521 in an iterative decoding operation of step 4521. FIG. 34illustrates the conversion of apriori bit LLRs into the symbol LLRdomain which are represented by the feedback symbol LLR parameters LLR₆₃^(sym,bit), LLR₆₂ ^(sym,bit), . . . , LLR₀ ^(sym,bit) 4203 (theright-most column in FIG. 33 ). An explanation of one example approachas to how the feedback symbol LLRs 4301 are calculated in step 4527 hasbeen previously described.

Note that in some examples a constant value of (LLR₅ ^(bit,in)+LLR₄^(bit,in)+LLR₃ ^(bit,in)+LLR₂ ^(bit,in)+LLR₁ ^(bit,in)+LLR₀ ^(bit,in))/2may be added to all 64 rows in FIG. 34 , without affecting the extrinsicLLRs that are ultimately generated by the overall soft demapping circuit1522. Adding this constant has the advantage of eliminating alldivisions by 2 and reducing the number of additions in the computationsof FIG. 34 , following some simplifications.

Conversion to PSK Symbol LLRs

It was assumed in FIG. 33 that each of the 2^(k+Qm) message combinations4201 has a corresponding PSK LLR. The PSK LLRs are generated (as in step4525 of FIG. 36 ) by the Convert to PSK symbol LLRs circuit 1501 asshown in FIG. 15 . This conversion, for a 16OS-QPSK scheme, takes (as instep 4509 of FIG. 36 ) as inputs M=16 correlator outputs 1525 for a(k+Q_(m)) 6-bit message and generates 2^(k+Qm)=64 PSK LLRs 1532 asoutputs. From earlier, it was shown that the phases of the M=16 complexcorrelator outputs 1525 are meant to contain the Q_(m)=2 MS bits ofinformation of the transmitted 6-bit message. For example, consider thecase where the true phase is −π/2 for a 6-bit message x. Now, it may beobserved that in normal channel conditions, one correlator output (mostprobably the correct I-Q pair), has a phase of −π/2, and the phasevalues of the remaining M−1=15 correlator outputs (most probably theincorrect I-Q pairs), will be uniformly distributed from the applicablerange of [−π, π). Therefore, if the true phase −π/2 is subtracted fromall the M=16 correlator output phases, at least one phase error isexpected to be near zero, and the rest of the phases are expected tohave random values in the above applicable range.

Note that while the QPSK phases [π/4, π/3, −π/4, −3 π/4] were used inthe datasets described earlier for the OS-only scheme, one exampletechnique will be introduced that allows these 16OS-QPSK datasets to begeneralised and used to model any PSK radix in the previous testbenchdiscussion. For the sake of simplicity, phase mappings that begin with aphase of 0 will be adopted, such as [0, π/2, −α/2, −π] for QPSK, in thisexample embodiment.

On the other side, the distributions of correct and incorrect phaseerror values may be considered. The phase errors calculated above(resulting from the subtraction of an ‘assumed’ true phase from the M=16received phases) may be applied to the probability density functions(PDFs) of both the distributions, in order to obtain the probabilitiesof each correlator output to be a) a correct correlator output or b) anincorrect correlator output. Using these conditional probabilities, theprobability ratios (i.e., the PSK LLRs) may be calculated for each ofthe M=16 correlator outputs, according to the formulae below:

${{PSK}{LLR}}\overset{\bigtriangleup}{=}{\ln\left\lbrack \frac{\Pr\left( {{correct}❘{{correlator}{output}}} \right)}{\Pr\left( {{incorrect}❘{{correlator}{output}}} \right)} \right\rbrack}$

Applying Bayes Theorem Gives

${{PSK}{LLR}} = {\ln\left\lbrack \frac{{\Pr\left( {{{correlator}{output}}❘{correct}} \right)} \times {\Pr({correct})}}{{\Pr\left( {{{correlator}{output}}❘{incorrect}} \right)} \times {\Pr({incorrect})}} \right\rbrack}$

Here, the conditional probabilities are characterised by the normal andthe uniform distributions, and it may be assumed that Pr (correct)=1/Mand Pr (incorrect)=(M−1)/M. Making these substitutions gives

${{PSK}{LLR}} = {\ln\left\lbrack \frac{{NormalPDF}\left( {{{phase}{error}},0,\sigma_{correct}} \right)}{0.5/\pi \times \left( {M - 1} \right)} \right\rbrack}$

Here, 0.5/π is the value of the uniform distribution across the range −πto +7. Note that here ‘phase error’ refers to the difference between thephase of the corresponding correlator output and the phase of thecorresponding one of the 2^(k+Qm) message combinations.

In the above example, it was assumed that the true phase is −π/2; i.e.,a fixed value was assumed for the 2 MS bits of the message. However,this assumption is made in the absence of any knowledge of what the truephase is, and hence, the above approach must be applied to all PSK phasepossibilities (that is 4 phases in a QPSK scheme). The steps in theconversion 1501 (as in step 4525 of FIG. 36 ) to PSK symbol LLRs 1532can therefore be summarised into the following: assume one possible PSKphase value (e.g. one value in [0, π/2, −π/2, −π] for QPSK), subtract itfrom the M correlator phases 1530, apply resulting phase error values tothe correct and incorrect PDFs, calculate the PSK LLR for eachcorrelator value from the PDF outputs, and repeat these steps from thebeginning with a new PSK phase value. This process of step 4525produces, in a 16OS-QPSK scheme, M.2^(Qm) or 16×4=64 PSK symbol LLRs1532, which correspond to the input PSK LLR parameters 4202 in FIG. 33shown as LLR₆₃ ^(PSK,in), LLR₆₂ ^(PSK,in), . . . , LLR₀ ^(PSK,in). Insummary, it can be said that the output phases 1530 of the M correlatoroutputs 1525 are combined with the second set of distribution parameters(σ_(phase)) 1523 of the aggregated correlator output phase distribution,in order to obtain in step 4525 a third set of apriori soft signalscomprising 2^(k+Qm) soft phases (PSK symbol LLRs 1532).

Summary

In summary, a soft demapping circuit 1522 has been proposed forperforming soft-decision demodulation in the receiver chain 1510 of atransmission system 1500 comprising a transmitter chain 1503, a channel1536 and a receiver chain 1510.

The transmitter chain 1503 signals a first set of bits 1508 comprising kbits by transmitting a spreading sequence 1511 that is selected from aset of 2^(k) possible signals according to the values of the k bits, andthe transmitter signals a second set of bits 1509 comprising Q_(m) bitsby rotating the phase of the spreading sequence 1511 using a rotationselected from a set of 2^(Qm) possible rotations according to the valuesof the Q_(m) bits in the modulator circuit 1504. The receiver chain 1510uses a bank of 2^(k) correlators to detect the transmission of eachpossible signal, and wherein the 2^(k) magnitudes 1531 of the correlatoroutputs 1525 are provided as a first set of inputs to the soft demappingcircuit 1522, and wherein a second set of apriori soft signals orfeedback bit LLRs 910 comprising k soft bits are provided as a secondset of inputs to the soft demapping circuit 1522. Furthermore, the 2^(k)phases 1530 of the correlator outputs 1525 are provided as a third setof inputs to the soft demapping circuit 1522, and a fourth set ofapriori soft signals or feedback bit LLRs 910 comprising Q_(m) soft bitsare provided as a fourth set of inputs to the soft demapping circuit1522. The soft demapping circuit 1522 calculates a first set ofaposteriori soft bits comprising k soft bits based on statistics andparameters 1520 derived from a plurality of aggregated correlator outputmagnitude distributions, and wherein the soft demapping circuit 1522calculates a second set of aposteriori soft bits comprising Q_(m) softbits based on statistics (the σ_(phase) parameter 1523) derived from aplurality of aggregated correlator output phase distributions.Furthermore, the soft demapping circuit 1522 combines (as in step 4528of FIG. 36 ) all apriori soft signals 908 1532 1534 to generate a set of2^(k+Qm) aposteriori soft signals or symbol LLRs 1529 and wherein theset of 2^(k+Qm) aposteriori soft signals or symbol LLRs 1529 arecombined (as in step 4513 of FIG. 36 ) to obtain the first set ofaposteriori soft bit LLRs 909 and the second set of aposteriori softbits. Following that, the first set of aposteriori soft bits arecombined with the soft bits of the second set of apriori soft signals,in order to obtain a first set of extrinsic soft bits. Finally, thesecond set of aposteriori soft bits are combined with the soft bits ofthe fourth set of apriori soft signals, in order to obtain a second setof extrinsic soft bits comprising Q_(m) soft bits.

The operation 4500 of the example soft demapper for the OS-PSK scheme,as demonstrated in the flowchart of FIG. 36 , may be summarised asfollows. Initially at 4501, the demapper receives 4502 a set of signalsas the outputs of the demodulator that correspond to a transmittedframe. Then, it is decided which of the three different methods ofestimating the distributions of the correlator output magnitudes andphases, are to be employed. If the offline approach of, say, step 4523is chosen, the characteristics of the channel, such as thesignal-to-noise ratio and channel type (e.g. AWGN), are identified instep 4505. The result of the identification is then used to address apre-computed look up table 1527 of parameters for the distributions ofthe correlator output magnitudes and phases. If, in contrast, an onlineapproach of distribution estimation of step 4524 is chosen, the choicewill be either the use of synchronisation sequences (as in step 4507 ofFIG. 36 ), or applying the largest magnitude of step 4508. Whicheverestimation approach is employed, the estimated parameters of themagnitude distributions, alongside the collected correlator outputmagnitudes of step 4509 of FIG. 36 , are used to calculate (as in step4510 of FIG. 36 ) the OS soft signals, which may be in the form of LLRs,as described previously. Similarly, the calculation in step 4525 of thePSK soft signals is performed using the correlator output phase valuesand the estimated parameters of the phase error distribution, asdescribed in the example embodiment for conversion to PSK symbol LLRs.

Following that, the calculated OS (as in step 4510 of FIG. 36 ) and PSK(as in step 4525) soft signals are stored (as in steps 4511 and 4526) ininternal memory, in case a demap-decode round of iterative decoding isrequired later. Since, only the first iteration has been started so far,of a possible iterative decoding process, there is no value on thefeedback path from the decoder. Hence, this feedback will be allzero-valued, as in step 4512 of FIG. 36 . The feedback path—albeit zerovalued as of now—is in the LLR domain (soft bits), and hence isconverted in step 4527 into the symbols domain to provide the feedbackapriori soft signals (as previously described with respect to theBit-symbol LLR circuit of a soft demapper). The OS and PSK soft signals,which were previously calculated in steps 4510 and 4525, are also of theapriori type, and combined with the feedback apriori soft signals, areused to calculate in step 4528 OS-PSK soft signals (as previouslydescribed with respect to the Symbol-to-symbol LLR circuit of a softdemapper). These signals are aposteriori information as they are afunction of the feedback path, despite so far being zero valued.

Next, the aposteriori OS-PSK symbols are converted in step 4513 into theLLRs domain to give the aposteriori soft bits (as previously describedwith respect to the Symbol-bit LLR circuit). This is followed byconverting in step 4514 the aposteriori soft bits into extrinsic softbits as the type required by, and sent in step 4515 to, the decoder.After the decoder is finished with the process of decoding the extrinsicinformation it received, the demapper receives in step 4516 the CRCstatus and the decoded soft bits from the decoder. Following a check instep 4517 of the CRC status, if it is failed in step 4521, turbodecoding is applied and the decoded soft bits received in step 4516 aretreated in step 4519 as apriori information fed back from the downstreamdecoder. Also, the OS and PSK soft signals, which had been calculatedpreviously in steps 4510 and 4525, are loaded in steps 4518 and 4529from memory as another set of apriori information for the seconddemapping iteration. The fed back apriori soft bits are converted instep 4527 into the soft signals domain, and the soft demapper uses allapriori information to make a second calculation (as in step 4528 ofFIG. 36 ) of aposteriori soft signals. The demap-decode iterations ofturbo decoding are ended in step 4522 either by a CRC pass or abandoningfurther decodes of the current frame, which may lead into, for example,a HARQ retransmission. At this point, the demapping of the current frameis ended in step 4520.

Testbench

Here, the testbench evaluates a soft demapping circuit 1522, for theOS-PSK scheme, and the testbench is demonstrated in the block diagram ofFIG. 18 , which illustrates the 16OS-PSK testbench using 16OS-QPSKdatasets. For a given dataset, the testbench 1800 generates threeextrinsic information transfer (EXIT) charts 1801 on different parts ofthe message bits/LLRs: namely the OS bits/LLRs of the OS flow 1802, thePSK bits/LLRs of the PSK flow 1803, and the combined OS-PSK bits/LLRs ofthe combined flow 1804 (i.e., the entire encoded/decoded message). Partsof the testbench 1800 that are in the set 113, 114, 904, 909, 1001,1501, 1506, 1507, 1508, 1509, 1511, 1515, 1517, 1521, 1522, 1524, 1526,1530, 1531, 1532, 1808, 1811, 1814, 1815 in FIG. 18 represent the flow1805, which is present in real transmission systems 1500, and theremaining parts are the flows 1806 exclusive to the testbench. Thetestbench 1800 in FIG. 18 has the same operation as the testbench 1000demonstrated in FIG. 10 .

As the datasets used in this current work's testbench 1800 are based onOS-PSK schemes, that is different from the earlier discussed OS-onlymodels and datasets 1012, the datasets 1807 and the functionality of theSimulate channel circuit 1900 in FIG. 18 are different from thecorresponding circuits 1012 1021 in the OS-only scheme. Example OS-PSKdatasets 1807 have been described and introduced previously, and theSimulate channel circuit 1900 described below. The above-listed parts inFIG. 18 share the same circuits with the block diagram of FIG. 15 ,except that the hard demapper circuit 1808 is added (as it was for theOS-only scheme) in this testbench 1800 so that the bit error rates (BER)1809 of the hard decision demapping flow 1812 is compared against those1810 of the soft decision demapping flow 1813.

Channel Simulation

In the example testbench 1800, a given channel is simulated in thesimulate channel circuit 1900 using its corresponding dataset, from theset of datasets 1807 presented earlier, which all belong to the16OS-QPSK scheme. In some examples, the testbench 1800 may be arrangedto simulate other PSK schemes; such as BPSK, 8PSK or 16PSK. For this, itis necessary to remove, from the datasets 1807, the dependence on theQPSK scheme. This can be performed by the method described for theOS-only scheme: for every pair of ‘1 16OS-QPSK symbol-16 correlator I-Qpairs’, the true phase embedded in the QPSK part of the 16OS-QPSK symbolvalue is subtracted from the phase of each correlator complex value (asthe received QPSK phase). This is shown in FIG. 19 , which illustratesthe 16OS-nPSK channel simulation using 16OS-QPSK dataset. To find outthe true phase value, the result of dividing 1901 the 16OS-QPSK symbolvalue by M=16 (with rounding 1902 towards zero) is used to choose thephase in the QPSK phase mapping circuit 1903. The testbench 1800 isgeneric with respect to the OS modulation order and can have any valueof M=2^(k).

Given that the 16OS-QPSK symbol values 4001 are in the range[0,2^(k+Qm)−1] or [0,63] (FIG. 31 ), the division 1901 by M=16 (followedby rounding 1902) will give a value in the range [0,2^(Qm)−1] or [0,3],that is equal to the Q_(m)=2 MS bits of 16OS-QPSK symbol's binary value.Subtraction of phases is performed by dividing 1904 the complex numberwith the received phase by a complex number of magnitude one 1905 andthe true phase value, as shown by the ‘÷’ operator in FIG. 19 . Withthis computation, the 16OS-QPSK dataset is transformed into a new set ofdata 1906 with 16OS symbols and PSK phase errors: the 16OS-PSK data.This transformation is performed offline 1909, shown by dotted lines inFIG. 19 . The flow during the simulation 1910 is shown by solid lines inFIG. 19 .

The new 16OS-PSK data 1906 can be used to simulate 16OS-PSK schemes withany degrees of PSK modulation; such as BSPK, 8PSK, or nPSK (n=2^(Qm)) inthe generic case. From the inputs to the circuit in FIG. 19 , k=4 bitsdefine the 16OS symbol value, and one row from the 16OS-PSK data 1906with the same input 16OS symbol value is randomly chosen. The M=16complex I-Q pairs in the corresponding row of the data are multiplied1907 by a complex number with a magnitude of one and a phase that isdefined by the other input to the simulate channel circuit 1900: theQ_(m) bits of an nPSK scheme (where n=2^(Qm)). This multiplication 1907inverses the effect of the division 1904 performed offline previously tocalculate the phase errors: the multiplication 1907 adds to the phaseerrors the phase from the nPSK scheme. The result is M=16 correlator I-Qpairs that become the output 1811 for the simulate channel circuit 1900.

Note that the phase mappings [π/4, 3π/4, −π/4, −3π/4] are always adoptedin the QPSK phase mapping circuit 1903 in FIG. 19 , in accordance withthe datasets described earlier in this section. By contrast, the nPSKphase mapping circuit 1908 in FIG. 19 adopts different phases dependingon which PSK modulation order is being simulated. For the sake ofsimplicity, a phase mapping that begins with a phase of ‘0’ is adopted.In the case of QPSK, the phase mapping [0, π/2, −π/2, −π] is adoptedhere, which preserves the Gray mapping, but with a rotation of π/4radians with respect to the datasets 1807 mentioned above. For BPSK [0,−π] is adopted, for 8PSK [0 1 3 2 −1 −2−4 −3]*π/4 is adopted, for 16PSK[0 1 3 2 7 6 4 5 −1−2 −4 −3 −8 −7 −5−6]*−π/8 is adopted and for 32PSK [01 3 2 7 6 4 5 15 14 12 13 8 9 11 10−1−2 −4 −3 −8 −7 −5 −6 −16 −15 −13−14 −9−10 −12−11]*π/16 is adopted, which all implement Gray mapping.

PSK Hard Demapping

It was mentioned earlier that a hard decision demapping flow 1812 isused in the testbench 1800 to compare the hard BERs 1809 with the softBERs 1810 in the EXIT charts 1801. The k=4 bits of the message modulatedby the OS scheme are demapped by the hard demapper circuit 1808 in thehard decision for symbol circuit 1814 by taking the index of thelargest-magnitude I-Q complex pair and converting it to binary in theconvert to bits circuit 1815. This is described in full detail above,for the OS-only scheme.

To find out Q_(m) bits of the message modulated by the PSK scheme, theHard Demapper circuit 1808 (FIG. 18 ) applies the following approach.The hard decision for symbol circuit 1814 first calculates thedifference between the phase of the largest-magnitude correlator I-Qpair (amongst the received M=16 correlator outputs) with each phase inthe phase mapping vector (e.g., vector [0, π/2, −π/2, −π] in QPSK) inthe applied PSK scheme. The hard decision for symbol circuit 1814 of thehard demapper circuit 1808 then takes the PSK phase that has the leastdifference with the phase of the largest-magnitude I-Q complex value asthe phase of the PSK symbol and converts the index of this phase tobinary according to the PSK's phase mapping vector in theconvert-to-bits circuit 1815. For example, it may be assumed that a QPSKmodulation with a mapping vector [0, π/2, −π/2, −π] is applied, and thephase of the largest-magnitude I-Q pair is 5π/3. With some calculations,it may be observed that the angle 5π/3 in the [0, 2π] range is closestto the angle −π/2 in the [−π, π] range (of the phase mapping). The value−π/2 has an index of 2 in QPSK mapping [0, π/2, −π/2, −π], and, hence,the hard demapper circuit 1808 binary value for the Q_(m)=2 MS bits ofthe 16OS-QPSK modulation in this example will be ‘10’.

Per-Scheme Quality Measurements

With the 16OS-PSK schemes that was simulated using the example testbench1800, it is possible to measure the quality parameters, not only of theresults representing all message bits in the combined flow 1804, butalso on parts of the message corresponding to each of the OS flow 1802and the PSK flow 1803. For example, in a 16OS-QPSK scheme with N bits ina code block in total, every k+Q_(m)=6 bits of the encoded bits 1001 ofthe transmitter and on the hard demapper's output bits 1035 willcomprise of k=4 16OS bits, Q_(m)=2 QPSK bits, and the total 6 16OS-QPSKbits—each of the three referred to as a bit group. The same can be said,in terms of LLR groups, for the bit LLRs generated from the softdemapper circuit 1522, which includes both the extrinsic bit LLRs 904and aposteriori bit LLRs 1042. The bit and LLR groups, when processedsimultaneously, are shown by three cascaded arrows, indicating the OSflow 1802, PSK flow 1803 and combined flow 1804 in FIG. 18 .

FIG. 20 demonstrates three EXIT charts for the three different 16OS-QPSKmodulation schemes. The middle plot 2001 in FIG. 20 corresponds to theQ_(m)=2 QPSK bits/bit LLRs of the first 6-bit transmission made duringthe processing of a set of N bits, and to the Q_(m)=2 QPSK bits/bit LLRsof the second transmission, and so on until the Q_(m)=2 QPSK bits/bitLLRs of the last transmission made during the processing of the N bits.The same can be said for the right-hand plot 2002 of FIG. 20 : the plotdata corresponds to the set of all k=4 16OS bits/bit LLRs where eachappear in a different transmission, amongst all transmissions, for Nbits.

Measuring 1036 the hard BERs 1809 for the 16OS-PSK, 16OS, and PSK flowsrequires encoded bits groups 1001 from the transmitter and the harddemapper's output bits 1035, as shown in FIG. 18 . The three soft BERvalues 1810 are computed 1005 from the encoded bits groups 1001 of thetransmitter chain (as the reference) and the aposteriori bit LLR groups1042 that are turned 1041 into hard bits 1816 (as the soft-then-hardbits). Measuring 1006 the mutual information histogram (MI) [1]parameter of the bit LLRs for the three modulation schemes in a messageis made possible by using the encoded bits groups 1001 from thetransmitter chain and the extrinsic bit LLR groups 904 from the softdemapping circuit 1522. These extrinsic bit LLR groups 904 are also usedto calculate 1007 the MI averaging parameter, as shown in FIG. 18 .

Results

FIG. 25 demonstrates the EXIT charts for the MP_−7.5 dB dataset fordifferent PSK modulation orders of QPSK 2501, 8PSK 2502, 16PSK 2503, and32PSK 2504. Only the EXIT charts 2500 for the worst-case SNR value of−7.5 dB were chosen for inclusion as higher SNRs resulted in all qualitymeasures (including MI values and the 1-BER figure) to be close to 1.Also, there was not much difference between the results from the AWGNand MP channels, so only the multipath channel charts 2500 wereincluded. Details of what information is included in the EXIT charts aredescribed above for the OS-only scheme.

EXIT Charts OS Charts—PSK Charts

From the EXIT charts 2500 it may be observed that increasing the PSKmodulation order, except for small changes, does not have much effect onthe quality of the 16OS LLRs characterised in the EXIT charts 2505. Thismeans that the model underlying the datasets 1807 could, to a greatextent, keep the modulation schemes independent from each other. Incontrast, increasing the PSK modulation order does have noticeableeffect on the quality of PSK bit LLRs characterised in the EXIT charts2506: the quality measures decrease with increasing PSK modulationorder. This is expected, as the increase in the number of modulatedphases increases the chances of error in both (i) making the precisephases in transmitted signals, and (ii) in identifying the correct phasefrom the more error-prone data.

It is worth noting that in the specific case of 16OS-QPSK, the OS bitLLRs and the PSK bit LLRs have similar quality to each other. In thehigher order PSK schemes, the PSK bit LLRs have lower quality than theOS bit LLRs.

The EXIT charts 2507 for the OS-PSK symbols are based on measurements onall bit LLRs of the combined flow 1804 (including both OS bit LLRs ofthe OS flow 1802 and PSK bit LLRs of the PSK flow 1803), and hencedemonstrate an average behaviour between the corresponding OS EXITcharts 2505 and PSK EXIT charts 2506 for each PSK modulation order. Forexample, for the 16OS-32PSK scheme at MI=0, while the histogram MImeasurements for the 16OS bit LLRs and 32PSK bit LLRs are 0.87 and 0.44,respectively, the 16OS-32PSK bit LLRs have a histogram MI value of 0.63,that is a value between the other two measurements. Here, the average isa weighted average—in the case of 16OS-32PSK, the OS bit LLRs carry only⅘ of the weight of the PSK bit LLRs.

In the discussion of the OS-only scheme, the EXIT charts 1300 1400 weregenerated 1000 from a single scheme (16OS) and the upper bounds on thecoding rate were represented by the area underneath the MI histogramplot. In this section, there are schemes with different PSK modulationorders, and hence different total number of transmitted bits for theschemes are present. For example, the 16OS-QPSK scheme of the EXIT chart2501 contains 4+2=6 bits per transmission, and the 16OS-8PSK scheme ofthe EXIT chart 2502 is based on 4+3=7 bits per transmission. However,while the number of encoded bits per transmission increases withincreasing PSK modulation order, the reliability of the transmissiondecreases, and a lower channel coding rate is needed. It may be expectedthat a ‘sweet spot’ can be found where the benefit of increasing thenumber of encoded bits per transmission maximally outweighs the cost ofrequiring reduced coding rate. Given that the coding rate is a functionof the total number of transmitted bits, in each 16OS-nPSK EXIT chart2500 the area below the histogram MI plot is multiplied by the totalnumber of bits in order to provide a common measure of informationtransfer that is comparable across different nPSK schemes with differentn. For example, in moving from the 16OS-QPSK EXIT chart 2501 to the16OS-8PSK EXIT chart 2502, although the MI plots decrease in value, butit may be observed that the upper bound 2508 in the achievable codingrate (for both with and without iterative feedback) increases. This isbecause, although the area below the histogram MI plot decreases in thismovement, the increase in the number of transmitted bits from 6 to 7causes a considerable jump in the maximum coding rate, from 5.71 to 6.26in the iterative case, for instance.

In general, it can be said that using higher order PSK allows moreencoded bits per symbol, but imposes a lower channel coding rate inorder to achieve reliable decoding—these two effects act against eachother, but to different degrees at different PSK modulation orders. Theresults suggest that the 16OS-16PSK scheme of the EXIT chart 2503, withmaximum achievable coding rates of 6.31 and 5.79 for with and withoutiterative feedback, respectively, can convey the most information.However, phase tracking can be expected to become more challenging forthis high PSK modulation order, which might favour a reduced value inpractice. Also, the 4 PSK bits are more error prone than the 4 OS bits,which might make the channel decoder optimisation more difficult. Bycontrast, it may be observed that in the 16OS-QPSK scheme of the EXITchart 2501, the 2 PSK bits and the 4 OS bits are equally error prone(more or less), and support reliable phase tracking, which might beexpected to yield a reduced implementation challenge.

One Example Application

Referring now to FIG. 37 , there is illustrated a typical computingsystem 4600 that may be employed to implement soft demapping accordingto some example embodiments of the invention. Computing systems of thistype may be used in wireless communication units. Those skilled in therelevant art will also recognize how to implement the invention usingother computer systems or architectures. Computing system 4600 mayrepresent, for example, a desktop, laptop or notebook computer,hand-held computing device (PDA, cell phone, palmtop, etc.), mainframe,server, client, or any other type of special or general purposecomputing device as may be desirable or appropriate for a givenapplication or environment. Computing system 4600 can include at leastone processors, such as a processor 4604. Processor 4604 can beimplemented using a general or special-purpose processing engine suchas, for example, a microprocessor, microcontroller or other controllogic. In this example, processor 4604 is connected to a bus 4602 orother communications medium. In some examples, computing system 4600 maybe a non-transitory tangible computer program product comprisingexecutable code stored therein for implementing soft demapping.

Computing system 4600 can also include a main memory 4608, such asrandom access memory (RAM) or other dynamic memory, for storinginformation and instructions to be executed by processor 4604. Mainmemory 4608 also may be used for storing temporary variables or otherintermediate information during execution of instructions to be executedby processor 4604. Computing system 4600 may likewise include a readonly memory (ROM) or other static storage device coupled to bus 4602 forstoring static information and instructions for processor 4604.

The computing system 4600 may also include information storage system4610, which may include, for example, a media drive 4612 and a removablestorage interface 4620. The media drive 4612 may include a drive orother mechanism to support fixed or removable storage media, such as ahard disk drive, a floppy disk drive, a magnetic tape drive, an opticaldisk drive, a compact disc (CD) or digital video drive (DVD) read orwrite drive (R or RW), or other removable or fixed media drive. Storagemedia 4618 may include, for example, a hard disk, floppy disk, magnetictape, optical disk, CD or DVD, or other fixed or removable medium thatis read by and written to by media drive 4612. As these examplesillustrate, the storage media 4618 may include a computer-readablestorage medium having particular computer software or data storedtherein.

In alternative embodiments, information storage system 4610 may includeother similar components for allowing computer programs or otherinstructions or data to be loaded into computing system 4600. Suchcomponents may include, for example, a removable storage unit 4622 andan interface 4620, such as a program cartridge and cartridge interface,a removable memory (for example, a flash memory or other removablememory module) and memory slot, and other removable storage units 4622and interfaces 4620 that allow software and data to be transferred fromthe removable storage unit 4618 to computing system 4600.

Computing system 4600 can also include a communications interface 4624.Communications interface 4624 can be used to allow software and data tobe transferred between computing system 4600 and external devices.Examples of communications interface 4624 can include a modem, a networkinterface (such as an Ethernet or other NIC card), a communications port(such as for example, a universal serial bus (USB) port), a PCMCIA slotand card, etc. Software and data transferred via communicationsinterface 4624 are in the form of signals which can be electronic,electromagnetic, and optical or other signals capable of being receivedby communications interface 4624. These signals are provided tocommunications interface 4624 via a channel 4628. This channel 4628 maycarry signals and may be implemented using a wireless medium, wire orcable, fibre optics, or other communications medium. Some examples of achannel include a phone line, a cellular phone link, an RF link, anetwork interface, a local or wide area network, and othercommunications channels.

In this document, the terms ‘computer program product’,‘computer-readable medium’ and the like may be used generally to referto media such as, for example, memory 4608, storage device 4618, orstorage unit 4622. These and other forms of computer-readable media maystore at least one instruction for use by processor 4604, to cause theprocessor to perform specified operations. Such instructions, generallyreferred to as ‘computer program code’ (which may be grouped in the formof computer programs or other groupings), when executed, enable thecomputing system 4600 to perform functions of embodiments of the presentinvention. Note that the code may directly cause the processor toperform specified operations, be compiled to do so, and/or be combinedwith other software, hardware, and/or firmware elements (e.g., librariesfor performing standard functions) to do so.

In an embodiment where the elements are implemented using software, thesoftware may be stored in a computer-readable medium and loaded intocomputing system 4600 using, for example, removable storage drive 4622,drive 4612 or communications interface 4624. The control logic (in thisexample, software instructions or computer program code), when executedby the processor 4604, causes the processor 4604 to perform thefunctions of the invention as described herein.

In the foregoing specification, the invention has been described withreference to specific examples of embodiments of the invention. It will,however, be evident that various modifications and changes may be madetherein without departing from the scope of the invention as set forthin the appended claims and that the claims are not limited to thespecific examples described above.

The connections as discussed herein may be any type of connectionsuitable to transfer signals from or to the respective nodes, units ordevices, for example via intermediate devices. Accordingly, unlessimplied or stated otherwise, the connections may for example be directconnections or indirect connections. The connections may be illustratedor described in reference to being a single connection, a plurality ofconnections, unidirectional connections, or bidirectional connections.However, different embodiments may vary the implementation of theconnections. For example, separate unidirectional connections may beused rather than bidirectional connections and vice versa. Also,plurality of connections may be replaced with a single connection thattransfers multiple signals serially or in a time multiplexed manner.Likewise, single connections carrying multiple signals may be separatedout into various different connections carrying subsets of thesesignals. Therefore, many options exist for transferring signals.

Those skilled in the art will recognize that the architectures depictedherein are merely exemplary, and that in fact many other architecturescan be implemented which achieve the same functionality.

Any arrangement of components to achieve the same functionality iseffectively ‘associated’ such that the desired functionality isachieved. Hence, any two components herein combined to achieve aparticular functionality can be seen as ‘associated with’ each othersuch that the desired functionality is achieved, irrespective ofarchitectures or intermediary components. Likewise, any two componentsso associated can also be viewed as being ‘operably connected,’ or‘operably coupled,’ to each other to achieve the desired functionality.

Furthermore, those skilled in the art will recognize that boundariesbetween the above-described operations merely illustrative. The multipleoperations may be combined into a single operation, a single operationmay be distributed in additional operations and operations may beexecuted at least partially overlapping in time. Moreover, alternativeembodiments may include multiple instances of a particular operation,and the order of operations may be altered in various other embodiments.

The present invention is herein described with reference to anintegrated circuit device comprising, say, a microprocessor configuredto perform the functionality of the soft demapper. However, it will beappreciated that the present invention is not limited to such integratedcircuit devices, and may equally be applied to integrated circuitdevices comprising any alternative type of operational functionality.Examples of such integrated circuit device comprising alternative typesof operational functionality may include, by way of example only,application-specific integrated circuit (ASIC) devices,field-programmable gate array (FPGA) devices, or integrated with othercomponents, etc. Furthermore, because the illustrated embodiments of thepresent invention may for the most part, be implemented using electroniccomponents and circuits known to those skilled in the art, details havenot been explained in any greater extent than that considered necessary,for the understanding and appreciation of the underlying concepts of thepresent invention and in order not to obfuscate or distract from theteachings of the present invention. Alternatively, the circuit and/orcomponent examples may be implemented as any number of separateintegrated circuits or separate devices interconnected with each otherin a suitable manner.

Also for example, the examples, or portions thereof, may implemented assoft or code representations of physical circuitry or of logicalrepresentations convertible into physical circuitry, such as in ahardware description language of any appropriate type.

Also, embodiments of the invention are not limited to physical devicesor units implemented in non-programmable hardware but can also beapplied in programmable devices or units able to perform the desiredsoft demapping by operating in accordance with suitable program code,such as minicomputers, personal computers, notepads, personal digitalassistants, electronic games, automotive and other embedded systems,cell phones and various other wireless devices, commonly denoted in thisapplication as ‘computer systems’.

However, other modifications, variations and alternatives are alsopossible. The specifications and drawings are, accordingly, to beregarded in an illustrative rather than in a restrictive sense.

In the claims, any reference signs placed between parentheses shall notbe construed as limiting the claim. The word ‘comprising’ does notexclude the presence of other elements or steps then those listed in aclaim. Furthermore, the terms ‘a’ or ‘an,’ as used herein, are definedas at least one than one. Also, the use of introductory phrases such as‘at least one’ and ‘at least one’ in the claims should not be construedto imply that the introduction of another claim element by theindefinite articles ‘a’ or ‘an’ limits any particular claim containingsuch introduced claim element to inventions containing only one suchelement, even when the same claim includes the introductory phrases ‘atleast one’ or ‘at least one’ and indefinite articles such as ‘a’ or‘an.’ The same holds true for the use of definite articles. Unlessstated otherwise, terms such as ‘first’ and ‘second’ are used toarbitrarily distinguish between the elements such terms describe. Thus,these terms are not necessarily intended to indicate temporal or otherprioritization of such elements. The mere fact that certain measures arerecited in mutually different claims does not indicate that acombination of these measures cannot be used to advantage. The word‘subset’ refers to a selection of elements from a set, where thatselection may comprise one, some or all of the elements in the set.

REFERENCES

-   [1] J. Hagenauer, “The exit chart—introduction to extrinsic    information transfer in iterative processing,” 2004 12th European    Signal Processing Conference, Vienna, 2004, pp. 1541-1548.-   [2] 3GPP TS 38.212, “NR; Multiplexing and channel coding”, v16.1.0,    March 2020.-   [3] Z. B. Kaykac Egilmez, L. Xiang, R. G. Maunder and L. Hanzo, “The    Development, Operation and Performance of the 5G Polar Codes,” in    IEEE Communications Surveys & Tutorials, vol. 22, no. 1, pp. 96-122,    First quarter 2020.-   [4] S. B. Wicker and V. K. Bhargava, eds. “Reed-Solomon codes and    their applications,” John Wiley & Sons, 1999.-   [5] J. Neasham, “Simulated cross-correlation dataset for the 16-ary    Orthogonal Signalling scheme,” Newcastle University, Oct. 1, 2020.-   [6] J. Neasham, “Simulated cross-correlation dataset for the 16-ary    Orthogonal Signalling-Phase Shift Keying scheme,” Newcastle    University, Oct. 1, 2020.-   [7] “Modulation using the 16-ary Orthogonal Signalling scheme, and    the 16-ary Orthogonal Signalling-Phase Shift Keying scheme,”    Newcastle University and Sonardyne International Ltd, 2020.

1-12. (canceled)
 13. A communication unit for performing soft-decisiondemodulation comprising a receiver, wherein the receiver is arranged toreceive a transmitted signal having a first set of bits comprising kbits that has been selected from a set of 2^(k) possible signalsaccording to values of the k bits, and includes a second set of bitscomprising Q_(m) bits based on a phase rotation of the transmittedsignal selected from a set of 2^(Qm) possible rotations wherein thereceiver comprises: a demodulator comprising a bank of 2^(k) correlatorsand configured to: detect a transmission of each possible transmittedsignal, and output 2^(k) phases of the correlator outputs as a third setof inputs; a de-mapper circuit coupled to the demodulator and configuredto: receive the third set of inputs: and determine statistics derivedfrom one aggregated correlator output phase distribution of the thirdset of inputs that approximates an aggregation of a 2^(k) distributionsof the output phases of the bank of 2^(k) correlators when thecorresponding one of the set of 2^(k) possible signals was selected asthe transmission signal; and calculate therefrom and output a second setof aposteriori soft bits comprising Q_(m) soft bits.
 14. Thecommunication unit of claim 13, wherein the aggregated correlator outputphase distribution is represented by a second set of distributionparameters.
 15. The communication unit of claim 14, wherein the secondset of distribution parameters comprises a spreading parameter,sigma_(phase).
 16. The communication unit of claim 13, wherein thedemodulator is further configured to output 2^(k) magnitudes ofcorrelator outputs, based on the detected possible transmitted signals,by the bank of 2^(k) correlators as a first set of inputs.
 17. Thecommunication unit of claim 16, wherein the de-mapper circuit isconfigured to perform at least one of the following: estimate the secondset of distribution parameters of the aggregated correlator output phasedistribution by fitting a fifth probability distribution to phase errorsof correlator outputs obtained by correlating received synchronisationsignals with correlators corresponding to known synchronisation signals;estimate the second set of distribution parameters of the aggregatedcorrelator output phase distribution by fitting a sixth probabilitydistribution to phase errors of correlator outputs having the greatestmagnitude among sets of 2^(k) correlator outputs obtained by the bank of2^(k) correlators; select the second set of distribution parameters ofthe aggregated correlator output phase distribution from a look-up-tablecoupled to the de-mapper circuit.
 18. The communication unit of claim17, wherein at least one of the fifth or sixth probability distributionsis a Gaussian distribution.
 19. The communication unit of claim 14,wherein the de-mapper circuit is configured to accept a fourth set ofapriori soft signals comprising Q_(m) soft bits as a fourth set ofinputs.
 20. The communication unit of claim 19, wherein the second setof aposteriori soft bits is combined with soft bits of the fourth set ofapriori soft signals to obtain a second set of extrinsic soft bitscomprising Q_(m) soft bits.
 21. The communication unit of claim 14,wherein the output phases of the 2^(k) correlators are combined with thesecond set of distribution parameters of the aggregated correlatoroutput phase distribution to obtain a third set of apriori soft signalscomprising 2^(k+Qm) soft phases.
 22. The communication unit of claim 21,wherein the communication unit combines all apriori soft signals togenerate a set of 2^(k+Qm) aposteriori soft signals and wherein the setof 2^(k+Qm) aposteriori soft signals is combined to obtain the secondset of aposteriori soft bits.
 23. A method for performing soft-decisiondemodulation comprising a communication unit having a receiver, thereceiver having a de-mapper circuit coupled to a demodulator thatcomprises a bank of 2^(k) correlators, the method at the receivercomprising: receiving a transmitted signal having a first set of bitscomprising k bits that has been selected from a set of 2^(k) possiblesignals according to values of the k bits and having a second set ofbits comprising Q_(m) bits based on a phase rotation of the transmittedsignal selected from a set of 2^(Qm) possible rotations, detecting atransmission of each possible transmitted signal, and outputting 2^(k)phases of the correlator outputs as a third set of inputs; receiving thethird set of inputs: and determining statistics derived from oneaggregated correlator output phase distribution of the third set ofinputs that approximates an aggregation of a 2^(k) distributions of theoutput phases of the bank of 2^(k) correlators when the correspondingone of the set of 2^(k) possible signals was selected as thetransmission signal; and calculating therefrom and output a second setof aposteriori soft bits comprising Q_(m) soft bits.
 24. The method ofclaim 23, further comprising representing the aggregated correlatoroutput phase distribution by a second set of distribution parameters.25. The method of claim 24, wherein the second set of distributionparameters comprises a spreading parameter, sigma_(phase).
 26. Themethod of claim 23, further comprising outputting 2^(k) magnitudes ofcorrelator outputs by the demodulator, based on the detected possibletransmitted signals, by the bank of 2^(k) correlators as a first set ofinputs.
 27. The method of claim 26, further comprising performing by thede-mapper circuit at least one of the following: estimating the secondset of distribution parameters of the aggregated correlator output phasedistribution by fitting a fifth probability distribution to phase errorsof correlator outputs obtained by correlating received synchronisationsignals with correlators corresponding to known synchronisation signals;estimating the second set of distribution parameters of the aggregatedcorrelator output phase distribution by fitting a sixth probabilitydistribution to phase errors of correlator outputs having the greatestmagnitude among sets of 2^(k) correlator outputs obtained by the bank of2^(k) correlators; selecting the second set of distribution parametersof the aggregated correlator output phase distribution from alook-up-table coupled to the de-mapper circuit.
 28. The method of claim27, wherein at least one of the fifth or sixth probability distributionsis a Gaussian distribution.
 29. The method of claim 12, furthercomprising accepting, by the de-mapper circuit, a fourth set of apriorisoft signals comprising Q_(m) soft bits as a fourth set of inputs. 30.The method of claim 17, further comprising combining the second set ofaposteriori soft bits with soft bits of the fourth set of apriori softsignals thereby obtaining a second set of extrinsic soft bits comprisingQ_(m) soft bits.
 31. The method of claim 24, further comprisingcombining the output phases of the 2^(k) correlators with the second setof distribution parameters of the aggregated correlator output phasedistribution thereby obtaining a third set of apriori soft signalscomprising 2^(k+Qm) soft phases.
 32. The method of claim 31, furthercomprising combining all apriori soft signals to generate a set of2^(k+Qm) aposteriori soft signals and combining the set of 2^(k+Qm)aposteriori soft signals thereby obtaining the second set of aposteriorisoft bits.